###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Biji Wong (Winter)

**Restrictions:** Open only to students in the B.Ed. program, 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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Restrictions:** Not open to students who have taken CEGEP course 201-101 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Lars Sektnan (Fall)

**Prerequisites:** A course in functions.

**Restrictions:** Not open to students who have taken or are taking MATH 130, MATH 131, MATH 139, MATH 140, MATH 150. MATH 139, MATH 140, MATH 141, MATH 150 and MATH 151 are not open to students who have taken or are taking MATH 122, except by special permission of the Department of Mathematics and Statistics. Open to Faculty of Management students only. Offered by the Faculty of Science. 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.

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Sidney Trudeau (Winter)

**Restrictions:** Not open to students who have taken or are taking MATH 223, or MATH 133 or CEGEP objective 00UQ or equivalent. Open to Faculty of Management students only. Offered by the Faculty of Science. Students intending to pursue one of the major or minor concentrations in Mathematics and Statistics in the Faculty of Management should take MATH 133 instead.

###### MATH 125 - Mathematical Techniques for Economics

Differentation of single and multivarible functions.;optimization of single and multivarible functions; constrained optimization of multivariable functions; elements of integration; applications to economics.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Restrictions:** Not open to students who have taken MATH 122 Calculus for Management or MATH 141 Calculus II.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Djivede Kelome, Francesco Dolce, Guohuan Qiu, Amit Sharma (Fall) Haining Wang (Winter)

**Prerequisites:** a course in functions

**Restrictions:** Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent. 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. Not open to students who are taking or have taken MATH 134.

###### 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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Restrictions:** Not open to students who are taking or have taken MATH 133

###### MATH 139 - Calculus 1 with Precalculus

Review of trigonometry and other Precalculus topics. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Abbas Mehrabian (Fall)

**Prerequisites:** a course in functions

**Restrictions:** Not open to students who have taken CEGEP objective 00UN or equivalent. Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics.

###### MATH 140 - Calculus 1

Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Sidney Trudeau, xianchang Meng, Ying Hu (Fall) Lars Sektnan (Winter)

**Prerequisites:** High School Calculus

**Restrictions:** Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent 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 141 - Calculus 2

The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Damien Gobin (Fall) Sidney Trudeau, Jonah Gaster, Thomas F Fox (Winter)

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

**Restrictions:** Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent 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 - Calculus A

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

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Charles Roth (Fall)

**Restrictions:** Not open to students who have taken CEGEP objective 00UN or equivalent 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 151 - Calculus B

Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Charles Roth (Winter)

**Prerequisites:** MATH 150

**Restrictions:** Not open to students who have taken CEGEP objective 00UP or equivalent 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 Not open to students who have taken MATH 152

###### 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

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Sidney Trudeau (Fall)

###### 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).

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Abbas Khalili Mahmoudabadi, David B Wolfson (Fall) Jose Andres Correa (Winter)

**Restrictions:** 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.

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Russell Steele (Winter)

**Prerequisites:** MATH 203 or equivalent. No calculus prerequisites

**Restrictions:** 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.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Stephen W Drury, Niko Laaksonen (Fall) Stephen W Drury (Winter)

**Prerequisites:** MATH 141. Familiarity with vector geometry or Corequisite

**Corequisites:** MATH 133

**Restrictions:** Not open to students who have taken CEGEP course 201-303 or MATH 150, MATH 151 or MATH 227

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Bogdan Lucian Nica (Fall) Djivede Kelome (Winter)

**Prerequisites:** MATH 133 or equivalent

**Restrictions:** 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

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Daniel Wise (Fall)

**Prerequisites:** MATH 133 or equivalent

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Bogdan Lucian Nica (Winter)

**Prerequisites:** MATH 235

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Philip Evan Decorte (Fall) Benjamin Seamone (Winter)

**Corequisites:** MATH 133.

**Restrictions:** For students in any Computer Science program. Others only with the instructor's permission. 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Jerome Vetois (Fall)

**Prerequisites:** MATH 141

**Restrictions:** Not open to students who are taking or who have taken MATH 254.

###### MATH 243 - Analysis 2

Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Axel W Hundemer (Winter)

**Prerequisites:** MATH 242 or MATH 254.

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Axel W Hundemer (Winter)

**Prerequisites:** MATH 133 or equivalent.

**Restrictions:** Intended for Honours Physics and Engineering students Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Pengfei Guan (Fall)

**Prerequisites:** MATH 133 and MATH 222 or consent of Department.

**Restrictions:** Intended for Honours Mathematics, Physics and Engineering students Not open to students who have taken or are taking MATH 314

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Charles Roth (Winter)

**Prerequisites:** MATH 248.

**Restrictions:** Intended for Honours Physics and Engineering students Not open to students who have taken or are taking MATH 316

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Jan Vonk (Winter)

**Prerequisites:** MATH 235 or permission of the Department

**Restrictions:** Not open to students who are taking or have taken MATH 247

###### MATH 254 - Honours Analysis 1

Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Axel W Hundemer (Fall)

**Prerequisites:** MATH 141

**Restrictions:** Not open to students who are taking or who have taken MATH 242.

###### MATH 255 - Honours Analysis 2

Basic point-set topology, metric spaces

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Rustum Choksi (Winter)

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

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Sidney Trudeau, Xinyang Lu (Fall) Stephen W Drury (Winter)

**Prerequisites:** MATH 141, MATH 133 or equivalent.

**Restrictions:** Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 151, MATH 152, OR MATH 222.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Jacques Claude Hurtubise, Jessica Lin (Fall) xianchang Meng, Rohit Jain (Winter)

**Corequisites:** MATH 262.

**Restrictions:** Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 315 or MATH 325.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Andy Wan (Fall) Pengfei Guan (Winter)

**Prerequisites:** MATH 262 or MATH 151 or MATH 152 or equivalent.

**Corequisites:** MATH 263

**Restrictions:** Open only to students in the Faculty of Engineering. Not open to students who are taking or have taken MATH 319 or MATH 475.

###### MATH 270 - Applied Linear Algebra

Introduction. Review of basic linear algebra. Vector spaces. Eigenvalues and eigenvectors of matrices. Linear operators.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Charles Roth (Fall)

**Prerequisites:** MATH 263, MATH 264.

###### MATH 314 - Advanced Calculus

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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Stephen W Drury (Fall) Charles Roth (Winter)

**Prerequisites:** MATH 133, MATH 222

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

###### MATH 315 - Ordinary Differential Equations

First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** Jean-Christophe Nave (Fall) Jean-Philippe Lessard (Winter)

**Prerequisites:** MATH 222.

**Corequisites:** MATH 133.

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

###### MATH 316 - Complex Variables

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

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** John A Toth (Fall)

**Prerequisites:** MATH 314 and MATH 243

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

###### MATH 317 - Numerical Analysis

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

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Peter Bartello (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

###### MATH 318 - Mathematical Logic

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

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Marcin Sabok (Fall)

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

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Jessica Lin (Winter)

**Prerequisites:** MATH 223 or MATH 236, MATH 314, MATH 315

###### MATH 320 - Differential Geometry

Review of Euclidean geometry. Local theory of plane and space curves

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

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

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018, Summer 2018

**Instructor:** David B Wolfson (Fall) Chien-Lin Su (Winter)

**Prerequisites:** MATH 141 or equivalent.

**Restrictions:** Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus Not open to students who have taken or are taking MATH 356

###### MATH 324 - Statistics

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

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Abbas Khalili Mahmoudabadi (Fall) Masoud Asgharian-Dastenaei (Winter)

**Prerequisites:** MATH 323 or equivalent

**Restrictions:** Not open to students who have taken or are taking MATH 357

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Antony Raymond Humphries (Winter)

**Prerequisites:** MATH 222.

**Restrictions:** Intended for Honours Mathematics, Physics and Engineering programs. Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315

###### MATH 326 - Nonlinear Dynamics and Chaos

Linear systems of differential equations, linear stability theory. Nonlinear systems

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Antony Raymond Humphries (Fall)

**Prerequisites:** MATH 222, MATH 223

**Restrictions:** Not open to students who have taken or are taking MATH 376

###### 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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

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

###### MATH 329 - Theory of Interest

Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Ivo Panayotov (Winter)

**Prerequisites:** MATH 141

###### MATH 335 - Computational Algebra

Computational aspects of modern algebra. Computing in groups

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 235 and MATH 236.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Thomas F Fox (Fall)

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Sergey Norin (Winter)

**Prerequisites:** MATH 235 or MATH 240 or MATH 242.

**Corequisites:** MATH 223 or MATH 236.

**Restrictions:** Not open to students who have taken or are taking MATH 343 or MATH 350.

###### MATH 346 - Number Theory

Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 235 or consent of instructor

**Restrictions:** Not open to students who have taken or are taking MATH 377.

###### MATH 348 - Topics in Geometry

Selected topics - the particular selection may vary from year to year. Topics include

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Thomas F Fox (Fall)

**Prerequisites:** 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Jan Volec (Fall)

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

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

###### 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.

**Credits:** 1

**Terms offered:** Fall 2017

**Instructor:** Sergey Norin (Fall)

**Prerequisites:** Enrolment in a math related program or permission of the instructor. Requires departmental approval. Enrolment in a math related program or permission of the instructor.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Linan Chen (Fall)

**Prerequisites:** MATH 133 or MATH 134, and MATH 222 or permisson of the Department.

**Corequisites:** MATH 242 or MATH 254

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** David B Wolfson (Winter)

**Prerequisites:** MATH 356 or equivalent

**Corequisites:** MATH 255 Honours Analysis 2

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

###### 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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 263, MATH 264.

**Restrictions:** Open only to students in the Faculty of Engineering.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Sarah Harrison (Fall)

**Prerequisites:** MATH 248.

**Corequisites:** MATH 454.

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

###### MATH 376 - Honours Nonlinear Dynamics

This course consists of the lectures of MATH 326, but will be assessed at the honours level.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Antony Raymond Humphries (Fall)

**Prerequisites:** MATH 222, MATH 223

**Restrictions:** Intended primarily for Honours students. Not open to students who have taken or are taking MATH 326.

###### MATH 377 - Honours Number Theory

This course consists of the lectures of MATH 346, but will be assessed at the honours level.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** Enrolment in Mathematics Honours program or consent of instructor

**Restrictions:** Not open to students who have taken or are taking MATH 346.

###### 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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 264

**Restrictions:** Open only to students in the Faculty of Engineering.

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Gantumur Tsogtgerel (Winter)

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

**Corequisites:** MATH 255 or MATH 243.

**Restrictions:** Intended primarily for Honours students.

###### MATH 396 - Undergraduate Research Project

Independent research project with a final written report.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Restrictions:** This course cannot be taken under the S/U option. Departmental permission required. Students cannot be supervised by the same instructor for two 396 Science courses. Open to students in programs offered by the Faculty of Science only.

###### MATH 397 - Honours Matrix Numerical Analysis

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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 251 or MATH 247, COMP 202 or permission of the instructor.

###### 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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

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

###### MATH 410 - Majors Project

A supervised project.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Djivede Kelome, Abbas Khalili Mahmoudabadi, Jean-Christophe Nave, David Stephens, Yi Yang (Fall) Djivede Kelome, Yi Yang, Russell Steele (Winter)

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

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Tim Hoheisel (Fall)

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

**Restrictions:** Not open to students who have taken or are taking MATH 487.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Axel W Hundemer, Michael Barr, Marcin Sabok (Fall) Axel W Hundemer, Tim Hoheisel, Dmitry Jakobson (Winter)

###### 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

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Yi Yang (Fall)

**Prerequisites:** MATH 324, and MATH 223 or MATH 236

**Restrictions:** Not open to students who have taken or are taking MATH 533.

###### MATH 427 - Statistical Quality Control

Introduction to quality management; variability and productivity. Quality measurement

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Christian Genest (Winter)

**Prerequisites:** MATH 323 + 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

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Djivede Kelome (Winter)

**Restrictions:** Not open to students who have taken MATH 330. Not open to students who have taken or are taking MATH 490.

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Anmar Khadra (Winter)

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

**Corequisites:** MATH 326 or MATH 376

###### 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Russell Steele (Winter)

**Prerequisites:** MATH 323

**Restrictions:** Not open to students who have taken or are taking MATH 547.

###### MATH 454 - Honours Analysis 3

Review of point-set topology

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Laurent Bruneau (Fall)

###### MATH 455 - Honours Analysis 4

Continuation of measure theory. Functional analysis

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Jerome Vetois (Winter)

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

###### MATH 456 - 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Eyal Z Goren (Fall)

**Restrictions:** Not open to students who have taken MATH 370.

###### MATH 457 - 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.

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Marcin Sabok (Winter)

**Restrictions:** Not open to students who have taken MATH 371.

###### MATH 458 - 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

**Credits:** 3

**Terms offered:** Winter 2018

**Instructor:** Jacques Claude Hurtubise (Winter)

**Restrictions:** Not open to students who have taken MATH 380.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

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

**Prerequisites:** appropriate honours courses with approval of the project supervisor

###### MATH 475 - 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.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Rustum Choksi (Fall)

**Restrictions:** Not open to students who have taken MATH 375.

###### 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.

**Credits:** 3

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Axel W Hundemer, Prakash Panangaden, Piotr Przytycki (Fall) Axel W Hundemer, Eyal Z Goren, Tim Hoheisel, Linan Chen, Bogdan Lucian Nica (Winter)

###### MATH 487 - Honours Mathematical Programming

The course consists of the lectures of MATH 417, but will be assessed at the honours level.

**Credits:** 3

**Terms offered:** Fall 2017

**Instructor:** Tim Hoheisel (Fall)

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

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

###### 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.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

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

###### MATH 490 - Honours Mathematics of Finance

This course consists of the lectures of MATH 430, but will be assessed at the honours level.

**Credits:** 3

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 222, MATH 323 or equivalent. (Intended primarily for honours students.)

**Restrictions:** Not open to students who have taken MATH 330. Not open to students who have taken or are taking MATH 430.

###### 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. Contingency tables

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Johanna Neslehova (Winter)

**Prerequisites:** MATH 423

**Restrictions:** Not open to students who have taken MATH 426

###### MATH 524 - Nonparametric Statistics

Distribution free procedures for 2-sample problem

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Christian Genest (Fall)

**Prerequisites:** MATH 324 or equivalent

**Restrictions:** Not open to students who have taken MATH 424

###### 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.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 324 or equivalent

**Restrictions:** Not open to students who have taken MATH 425

###### MATH 533 - Honours Regression and Analysis of Variance

This course consists of the lectures of MATH 423 but will be assessed at the 500 level.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Yi Yang (Fall)

**Prerequisites:** MATH 357, MATH 247 or MATH 251.

**Restrictions:** Not open to have taken or are taking MATH 423.

###### 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.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Anmar Khadra (Winter)

**Prerequisites:** MATH 325, MATH 356, MATH 376, a CEGEP or higher-level computer programming course.

**Restrictions:** Not open to students who have taken MATH 437.

###### 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.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 323 or equivalent and MATH 329

###### 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.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 323 and MATH 324 or equivalent

###### 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** David Stephens (Fall)

**Prerequisites:** MATH 324 or MATH 357 or equivalent

###### MATH 547 - Stochastic Processes

Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Dana Louis Addario-Berry (Winter)

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

**Restrictions:** Not open to students who have taken or are taking MATH 447.

###### MATH 550 - Combinatorics

Enumerative combinatorics

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Sergey Norin (Winter)

**Restrictions:** Permission of instructor.

###### MATH 552 - Combinatorial Optimization

Algorithmic and structural approaches in combinatorial optimization with a focus upon theory and applications. Topics include

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Yaqiao Li (Winter)

**Prerequisites:** MATH 350 or COMP 362 (or equivalent).

**Restrictions:** Not open to students who have taken or are taking COMP 552.

###### 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Adrian Roshan Vetta (Fall)

**Prerequisites:** COMP 362 or MATH 350 or MATH 454 or MATH 487, or instructor permission.

**Restrictions:** Not open to students who are taking or have taken COMP 553

###### 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.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 315 and MATH 319 or equivalent

###### 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Masoud Asgharian-Dastenaei (Fall)

**Prerequisites:** 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.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Abbas Khalili Mahmoudabadi (Winter)

**Prerequisites:** 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.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Tim Hoheisel (Winter)

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

###### MATH 564 - Advanced Real Analysis 1

Review of theory of measure and integration; product measures, Fubini's theorem; Lp 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Vojkan Jaksic (Fall)

**Prerequisites:** MATH 454, MATH 455 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 Rn, Fourier series and integrals, additional topics.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** John A Toth (Winter)

**Prerequisites:** 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.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 366 (formerly MATH 466), 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.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 455 or equivalent.

###### 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Henri Darmon (Fall)

**Prerequisites:** MATH 457 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.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Henri Darmon (Winter)

**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

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Jean-Philippe Lessard (Fall)

**Prerequisites:** MATH 325 and MATH 454 or permission of the instructor.

###### 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Daniel Wise (Fall)

**Prerequisites:** MATH 454

###### 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.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Niky Kamran (Winter)

**Prerequisites:** 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Jean-Christophe Nave (Fall)

**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

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Adam Oberman (Winter)

**Prerequisites:** MATH 475 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Rustum Choksi (Fall)

**Prerequisites:** MATH 475 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.

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Dmitry Jakobson (Winter)

**Prerequisites:** MATH 455 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.

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Linan Chen (Fall)

**Prerequisites:** MATH 356 and MATH 255 or MATH 243 or equivalent.

###### MATH 589 - Advanced Probability Theory 2

Characteristic functions

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**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.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 318, either MATH 455 or MATH 457, or permission of the instructor.

**Restrictions:** Not open to students who have taken or are taking MATH 488.

###### 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

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 488 or equivalent or consent of instructor

###### 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

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 488 or equivalent or consent of instructor

###### MATH 595 - Topics in Analysis

This course covers a topic in analysis.

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** John A Toth (Fall) Vojkan Jaksic (Winter)

**Prerequisites:** At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 454 or MATH 366. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

**Restrictions:** 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.

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Maksym Radziwill, Bogdan Lucian Nica (Fall) Eyal Z Goren, Daniel Wise (Winter)

**Prerequisites:** At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 456 or MATH 377. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

**Restrictions:** Requires permission of the Department of Mathematics and Statistics.

###### MATH 597 - Topics in Applied Mathematics

This course covers a topic in applied mathematics.

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** 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.

**Restrictions:** 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.

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Johanna Neslehova (Fall) David Stephens (Winter)

**Prerequisites:** 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.

**Restrictions:** 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.

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Jacques Claude Hurtubise, Niky Kamran (Fall) Piotr Przytycki (Winter)

**Prerequisites:** At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 454 and MATH 458. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.

**Restrictions:** Requires permission of the Department of Mathematics and Statistics.

###### MATH 600 - Master's Thesis Research 1

Graduate Studies

**Credits:** 6

**Terms offered:** Fall 2017, Winter 2018

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

**Restrictions:** Not open to students who have taken or are taking MATH 640

###### MATH 601 - Master's Thesis Research 2

Graduate Studies

**Credits:** 6

**Terms offered:** Fall 2017, Winter 2018

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

###### MATH 602 - Master's Research Preparation

Graduate Studies

**Credits:** 6

**Terms offered:** Fall 2017

**Instructor:** Dmitry Jakobson (Fall)

**Restrictions:** Open only to students with appropriate background.

###### MATH 604 - Master's Thesis Research 3

Graduate Studies

**Credits:** 6

**Terms offered:** Fall 2017, Winter 2018

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

###### MATH 605 - Master's Thesis Research 4

Graduate Studies

**Credits:** 6

**Terms offered:** Fall 2017, Winter 2018

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

###### MATH 635 - Functional Analysis 1

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 564, MATH 565, and MATH 566

###### MATH 638 - Partial Differential Equations 4

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** Math 581

###### MATH 640 - Project 1

Graduate Studies

**Credits:** 8

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Dmitry Jakobson (Fall) Dmitry Jakobson (Winter)

**Restrictions:** Not open to students who have taken or are taking MATH 600

###### MATH 641 - Project 2

Graduate Studies

**Credits:** 8

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Dmitry Jakobson (Fall) Dmitry Jakobson (Winter)

###### MATH 666 - Seminar Mathematics and Statistics 1

Graduate Studies

**Credits:** 2

**Terms offered:** Fall 2017

**Instructor:** Henri Darmon (Fall)

**Restrictions:** Departmental approval required.

###### MATH 667 - Seminar Mathematics and Statistics 2

Graduate Studies

**Credits:** 2

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Restrictions:** Departmental approval required.

###### MATH 671 - Applied Stochastic Processes

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 680 - Computation Intensive Statistics

Graduate Studies

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Yi Yang (Winter)

**Prerequisites:** MATH 556, MATH 557 or permission of instructor

###### MATH 681 - Time Series Analysis

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

**Prerequisites:** MATH 545 or equivalent

###### MATH 686 - Survival Analysis

Graduate Studies

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Masoud Asgharian-Dastenaei (Winter)

**Prerequisites:** MATH 556, MATH 557 or permission of instructor

###### MATH 687 - Reading Course in Mathematical Logic

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 689 - Reading Course in Algebra

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 690 - Reading Course in Number Theory

Graduate Studies

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Maksym Radziwill (Fall)

###### MATH 691 - Reading Course in Geometry/Topology

Graduate Studies

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Jacques Claude Hurtubise (Fall) Niky Kamran (Winter)

###### MATH 693 - Reading Course in Analysis

Graduate Studies

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Dana Louis Addario-Berry, Linan Chen (Fall) Linan Chen (Winter)

###### MATH 695 - Reading Course in Applied Mathematics

Graduate Studies

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Rustum Choksi (Fall)

###### MATH 697 - Reading Course in Statistics

Graduate Studies

**Credits:** 4

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Alexandra Schmidt, Sahir Bhatnagar (Fall) Johanna Neslehova, Linan Chen (Winter)

###### MATH 699 - Reading Course in Discrete Mathematics

Graduate Studies

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Sergey Norin (Fall)

###### MATH 700 - Ph.D. Preliminary Examination

Graduate Studies

**Credits:**

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Dmitry Jakobson (Fall) Dmitry Jakobson (Winter)

###### MATH 701 - Ph.D. Preliminary Examination

Graduate Studies

**Credits:**

**Terms offered:** Fall 2017, Winter 2018

**Instructor:** Dmitry Jakobson (Fall) Dmitry Jakobson (Winter)

###### MATH 704 - Advanced Topics in Mathematical Logic

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 706 - Advanced Topics in Geometry and Topology 1

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 707 - Advanced Topics in Geometry and Topology 2

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 720 - Advanced Topics in Algebra 1

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 721 - Advanced Topics in Algebra 2

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 722 - Advanced Topics in Algebraic Geometry

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 723 - Advanced Topics in Group Theory

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 726 - Advanced Topics in Number Theory

Graduate Studies

**Credits:** 4

**Terms offered:** Winter 2018

**Instructor:** Corentin Perret-Gentil-dit-Maillard (Winter)

###### MATH 727 - Advanced Topics in Arithmetic Geometry

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 740 - Advanced Topics in Analysis 1

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 741 - Advanced Topics in Analysis 2

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 742 - Advanced Topics in Mathematical Physics

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 743 - Advanced Topics in Microlocal Analysis

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 744 - Advanced Topics in Spectral Theory

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 756 - Advanced Topics in Optimization

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 758 - Advanced Topics in Discrete Mathematics

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 761 - Advanced Topics in Applied Mathematics 1

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 762 - Advanced Topics in Applied Mathematics 2

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 763 - Advanced Topics in Differential Equations

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 764 - Advanced Topics in Partial Differential Equations

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 765 - Advanced Topics in Numerical Analysis

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 782 - Advanced Topics in Statistics 1

Graduate Studies

**Credits:** 4

**Terms offered:** Fall 2017

**Instructor:** Russell Steele (Fall)

###### MATH 783 - Advanced Topics in Statistics 2

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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

###### MATH 784 - Advanced Topics in Probability

Graduate Studies

**Credits:** 4

**Terms offered:** This course is not scheduled for the 2017-2018 academic year.

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