###### MATH 111 - Mathematics for Education Students - Winter 2019 - Section 001

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

**Instructor:** TBA

**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 122 - Calculus for Management - Fall 2018 - Section 001

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

**Instructor:** Sidney Trudeau

**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 122 - Calculus for Management - Winter 2019 - Section 001

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

**Instructor:** Jeremy David Macdonald

**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 - Fall 2018 - Section 001

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

**Instructor:** Lars Martin Sektnan

**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 123 - Linear Algebra and Probability - Winter 2019 - Section 001

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

**Instructor:** TBA

**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 133 - Linear Algebra and Geometry - Fall 2018 - Section 001

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

**Instructor:** Jérôme Fortier

**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 133 - Linear Algebra and Geometry - Fall 2018 - Section 002

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

**Instructor:** Liangming Shen

**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 133 - Linear Algebra and Geometry - Fall 2018 - Section 003

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

**Instructor:** Yann Batiste Pequignot

**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 133 - Linear Algebra and Geometry - Fall 2018 - Section 004

**Credits:** 3

**Instructor:** Damian Login Osajda

**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 133 - Linear Algebra and Geometry - Winter 2019 - Section 001

**Credits:** 3

**Instructor:** Jérôme Fortier

**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 139 - Calculus 1 with Precalculus - Fall 2018 - Section 001

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

**Credits:** 4

**Instructor:** Lars Martin Sektnan, Sidney Trudeau

**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 - Fall 2018 - Section 001

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

**Credits:** 3

**Instructor:** Sidney Trudeau

**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 140 - Calculus 1 - Fall 2018 - Section 002

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

**Credits:** 3

**Instructor:** Jérôme Fortier

**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 140 - Calculus 1 - Fall 2018 - Section 003

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

**Credits:** 3

**Instructor:** Rebecca Patrias

**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 140 - Calculus 1 - Winter 2019 - Section 001

**Credits:** 3

**Instructor:** TBA

**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 - Fall 2018 - Section 001

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

**Credits:** 4

**Instructor:** Jonah Benjamin Gaster

**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 141 - Calculus 2 - Fall 2018 - Section 002

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

**Credits:** 4

**Instructor:** Corentin Perret-Gentil-dit-Maillard

**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 141 - Calculus 2 - Winter 2019 - Section 001

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

**Credits:** 4

**Instructor:** Jérôme Fortier

**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 141 - Calculus 2 - Winter 2019 - Section 002

**Credits:** 4

**Instructor:** TBA

**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 141 - Calculus 2 - Winter 2019 - Section 003

**Credits:** 4

**Instructor:** Sidney Trudeau

**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 - Fall 2018 - Section 001

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

**Credits:** 4

**Instructor:** Charles Roth

**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 - Winter 2019 - Section 001

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

**Credits:** 4

**Instructor:** Charles Roth

**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 - Fall 2018 - Section 001

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.

**Credits:** 3

**Instructor:** Sidney Trudeau

###### MATH 203 - Principles of Statistics 1 - Fall 2018 - Section 001

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

**Instructor:** Abbas Khalili Mahmoudabadi, David B Wolfson

**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 203 - Principles of Statistics 1 - Fall 2018 - Section 002

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

**Instructor:** Abbas Khalili Mahmoudabadi, David B Wolfson

**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 203 - Principles of Statistics 1 - Winter 2019 - Section 001

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

**Instructor:** David B Wolfson

**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 - Winter 2019 - Section 001

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

**Instructor:** Christian Genest

**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 - Fall 2018 - Section 001

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

**Instructor:** Dmitry Faifman

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

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

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

###### MATH 222 - Calculus 3 - Fall 2018 - Section 002

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

**Instructor:** Jeremy David Macdonald

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

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

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

###### MATH 222 - Calculus 3 - Winter 2019 - Section 001

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

**Instructor:** TBA

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

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

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

###### MATH 223 - Linear Algebra - Fall 2018 - Section 001

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

**Instructor:** Djivede Armel Kelome

**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 223 - Linear Algebra - Fall 2018 - Section 002

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

**Instructor:** Djivede Armel Kelome

**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 223 - Linear Algebra - Winter 2019 - Section 001

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

**Instructor:** Jeremy David Macdonald

**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 228 - Classical Geometry - Fall 2018 - Section 001

This course is designed to reintroduce classical Euclidean geometry to tomorrow’s teachers. Topics include: Axioms and Euclid’s Elements, the triangle theorem, the Pythagorean Theorem and its extensions, basic constructions and similar triangles, Thales’ theorems and cyclic quadrilaterals, the centers of triangles, the nine-point circle, conic sections and analytic geometry, the prismatoid formula, the Platonic solids, non-Euclidean geometries.

**Credits:** 3

**Instructor:** Thomas F Fox

**Restrictions:** Cannot be taken for credit by students in Mathematics and Statistics programs.

###### MATH 235 - Algebra 1 - Fall 2018 - Section 001

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

**Instructor:** Daniel T. Wise

**Prerequisites:** MATH 133 or equivalent

###### MATH 236 - Algebra 2 - Winter 2019 - Section 001

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

**Instructor:** TBA

**Prerequisites:** MATH 235

###### MATH 240 - Discrete Structures 1 - Fall 2018 - Section 001

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

**Instructor:** Jeremy David Macdonald

**Corequisites:** MATH 133.

**Restrictions:** For students in any Computer Science, Computer Engineering, or Software Engineering programs. Others only with the instructor's permission. Not open to students who have taken or are taking MATH 235.

###### MATH 240 - Discrete Structures 1 - Fall 2018 - Section 002

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

**Instructor:** Bogdan Nica

**Corequisites:** MATH 133.

**Restrictions:** For students in any Computer Science, Computer Engineering, or Software Engineering programs. Others only with the instructor's permission. Not open to students who have taken or are taking MATH 235.

###### MATH 240 - Discrete Structures 1 - Winter 2019 - Section 001

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

**Instructor:** TBA

**Corequisites:** MATH 133.

**Restrictions:** For students in any Computer Science, Computer Engineering, or Software Engineering programs. Others only with the instructor's permission. Not open to students who have taken or are taking MATH 235.

###### MATH 240 - Discrete Structures 1 - Winter 2019 - Section 002

**Credits:** 3

**Instructor:** Jeremy David Macdonald

**Corequisites:** MATH 133.

**Restrictions:** For students in any Computer Science, Computer Engineering, or Software Engineering programs. Others only with the instructor's permission. Not open to students who have taken or are taking MATH 235.

###### MATH 242 - Analysis 1 - Fall 2018 - Section 001

A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.

**Credits:** 3

**Instructor:** Jerome Vetois

**Prerequisites:** MATH 141

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

###### MATH 243 - Analysis 2 - Winter 2019 - Section 001

Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.

**Credits:** 3

**Instructor:** Axel W Hundemer

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

###### MATH 247 - Honours Applied Linear Algebra - Winter 2019 - Section 001

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

**Instructor:** Tim Hoheisel

**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 - Fall 2018 - Section 001

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

**Instructor:** Pengfei Guan

**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 - Winter 2019 - Section 001

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

**Instructor:** Charles Roth

**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 - Winter 2019 - Section 001

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

**Instructor:** TBA

**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 - Fall 2018 - Section 001

Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.

**Credits:** 3

**Instructor:** Axel W Hundemer

**Prerequisites:** MATH 141

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

###### MATH 255 - Honours Analysis 2 - Winter 2019 - Section 001

Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, HÃ¶lder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.

**Credits:** 3

**Instructor:** Rustum Choksi

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

###### MATH 262 - Intermediate Calculus - Fall 2018 - Section 001

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

**Instructor:** Vincent Létourneau

**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 262 - Intermediate Calculus - Fall 2018 - Section 002

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

**Instructor:** Stephen W Drury

**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 262 - Intermediate Calculus - Fall 2018 - Section 003

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

**Instructor:** Saikat Mazumdar

**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 262 - Intermediate Calculus - Winter 2019 - Section 001

**Credits:** 3

**Instructor:** Charles Roth

**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 - Fall 2018 - Section 001

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

**Instructor:** Jessica Lin

**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 263 - Ordinary Differential Equations for Engineers - Fall 2018 - Section 002

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

**Instructor:** Jessica Lin

**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 263 - Ordinary Differential Equations for Engineers - Winter 2019 - Section 001

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

**Instructor:** Sidney Trudeau

**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 263 - Ordinary Differential Equations for Engineers - Winter 2019 - Section 002

**Credits:** 3

**Instructor:** TBA

**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 - Fall 2018 - Section 001

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

**Instructor:** Ming Mei

**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 264 - Advanced Calculus for Engineers - Winter 2019 - Section 001

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

**Instructor:** Pengfei Guan

**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 271 - Linear Algebra and Partial Differential Equations - Fall 2018 - Section 001

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

**Credits:** 3

**Instructor:** Charles Roth

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

###### MATH 314 - Advanced Calculus - Fall 2018 - Section 001

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

**Instructor:** Charles Roth

**Prerequisites:** MATH 133, MATH 222

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

###### MATH 314 - Advanced Calculus - Winter 2019 - Section 001

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

**Instructor:** Stephen W Drury

**Prerequisites:** MATH 133, MATH 222

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

###### MATH 315 - Ordinary Differential Equations - Fall 2018 - Section 001

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

**Credits:** 3

**Instructor:** Jean-Christophe Nave

**Prerequisites:** MATH 222.

**Corequisites:** MATH 133.

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

###### MATH 315 - Ordinary Differential Equations - Winter 2019 - Section 001

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

**Credits:** 3

**Instructor:** Antony Raymond Humphries

**Prerequisites:** MATH 222.

**Corequisites:** MATH 133.

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

###### MATH 316 - Complex Variables - Fall 2018 - Section 001

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

**Credits:** 3

**Instructor:** Bogdan Nica

**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 - Fall 2018 - Section 001

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

**Credits:** 3

**Instructor:** Peter Bartello

**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 - Fall 2018 - Section 001

Propositional logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.

**Credits:** 3

**Instructor:** Marcin Sabok

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

###### MATH 319 - Introduction to Partial Differential Equations - Winter 2019 - Section 001

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

**Instructor:** Jessica Lin

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

###### MATH 323 - Probability - Fall 2018 - Section 001

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

**Instructor:** David Alan Stephens

**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 323 - Probability - Winter 2019 - Section 001

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

**Instructor:** David B Wolfson

**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 - Fall 2018 - Section 001

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

**Credits:** 3

**Instructor:** Abbas Khalili Mahmoudabadi

**Prerequisites:** MATH 323 or equivalent

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

###### MATH 324 - Statistics - Winter 2019 - Section 001

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

**Credits:** 3

**Instructor:** Masoud Asgharian-Dastenaei

**Prerequisites:** MATH 323 or equivalent

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

###### MATH 325 - Honours Ordinary Differential Equations - Winter 2019 - Section 001

First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.

**Credits:** 3

**Instructor:** Jean-Philippe Lessard

**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 - Fall 2018 - Section 001

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.

**Credits:** 3

**Instructor:** Jean-Philippe Lessard

**Prerequisites:** MATH 222, MATH 223

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

###### MATH 327 - Matrix Numerical Analysis - Winter 2019 - Section 001

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

**Instructor:** TBA

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

###### MATH 329 - Theory of Interest - Winter 2019 - Section 001

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

**Credits:** 3

**Instructor:** Djivede Armel Kelome

**Prerequisites:** MATH 141

###### MATH 338 - History and Philosophy of Mathematics - Fall 2018 - Section 001

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

**Instructor:** Thomas F Fox

###### MATH 340 - Discrete Structures 2 - Winter 2019 - Section 001

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

**Instructor:** Jérôme Fortier

**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 - Winter 2019 - Section 001

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

**Credits:** 3

**Instructor:** Michael Lipnowski

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

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

###### MATH 348 - Euclidean Geometry - Fall 2018 - Section 001

Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.

**Credits:** 3

**Instructor:** Piotr Przytycki

**Prerequisites:** MATH 133 or equivalent or permission of instructor.

**Restrictions:** Not open to students who have taken MATH 398.

###### MATH 350 - Graph Theory and Combinatorics - Fall 2018 - Section 001

Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.

**Credits:** 3

**Instructor:** Adrian Roshan Vetta

**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 356 - Honours Probability - Fall 2018 - Section 001

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

**Instructor:** Linan Chen

**Prerequisites:** MATH 243 or MATH 255, and MATH 222 or permission of the Department.

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

###### MATH 357 - Honours Statistics - Winter 2019 - Section 001

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

**Instructor:** Masoud Asgharian-Dastenaei

**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 376 - Honours Nonlinear Dynamics - Fall 2018 - Section 001

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

**Credits:** 3

**Instructor:** Jean-Philippe Lessard

**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 - Winter 2019 - Section 001

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

**Credits:** 3

**Instructor:** Michael Lipnowski

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

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

###### MATH 397 - Honours Matrix Numerical Analysis - Winter 2019 - Section 001

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

**Instructor:** TBA

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

###### MATH 398 - Honours Euclidean Geometry - Fall 2018 - Section 001

Honours level: points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.

**Credits:** 3

**Instructor:** Piotr Przytycki

**Prerequisites:** MATH 133 or equivalent or permission of instructor.

**Restrictions:** Not open to students taking or have take MATH 348.

###### MATH 417 - Linear Optimization - Fall 2018 - Section 001

An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory.

**Credits:** 3

**Instructor:** Van Quang Nguyen

**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 or MATH 517.

###### MATH 423 - Regression and Analysis of Variance - Fall 2018 - Section 001

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.

**Credits:** 3

**Instructor:** Yi Yang

**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 - Winter 2019 - Section 001

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.

**Credits:** 3

**Instructor:** TBA

**Prerequisites:** MATH 323 + MATH 324

###### MATH 430 - Mathematical Finance - Winter 2019 - Section 001

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.

**Credits:** 3

**Instructor:** Djivede Armel Kelome

**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 - Winter 2019 - Section 001

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

**Instructor:** Anmar Khadra

**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 - Winter 2019 - Section 001

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

**Instructor:** Russell Steele

**Prerequisites:** MATH 323

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

###### MATH 454 - Honours Analysis 3 - Fall 2018 - Section 001

Review of point-set topology: topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. Fubini-Tonelli theorem.

**Credits:** 3

**Instructor:** Dmitry Jakobson

###### MATH 455 - Honours Analysis 4 - Winter 2019 - Section 001

Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.

**Credits:** 3

**Instructor:** Jerome Vetois

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

###### MATH 456 - Honours Algebra 3 - Fall 2018 - Section 001

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

**Instructor:** Michael Yves Michel Pichot

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

###### MATH 457 - Honours Algebra 4 - Winter 2019 - Section 001

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

**Instructor:** Michael Yves Michel Pichot

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

###### MATH 458 - Honours Differential Geometry - Winter 2019 - Section 001

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.

**Credits:** 3

**Instructor:** Jacques Claude Hurtubise

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

###### MATH 466 - Honours Complex Analysis - Fall 2018 - Section 001

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

**Instructor:** Sarah Harrison

**Prerequisites:** MATH 248.

**Corequisites:** MATH 454.

**Restrictions:** Not open to students who have taken or are taking MATH 366, MATH 249, MATH 316 and MATH 381.

###### MATH 475 - Honours Partial Differential Equations - Fall 2018 - Section 001

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

**Instructor:** Rustum Choksi

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

###### MATH 478 - Computational Methods in Applied Mathematics - Winter 2019 - Section 001

Solution to initial value problems: Linear, Nonlinear Finite Difference Methods: accuracy and stability, Lax equivalence theorem, CFL and von Neumann conditions, Fourier analysis: diffusion, dissipation, dispersion, and spectral methods. Solution of large sparse linear systems: iterative methods, preconditioning, incomplete LU, multigrid, Krylov subspaces, conjugate gradient method. Applications to, e.g., weighted least squares, duality, constrained minimization, calculus of variation, inverse problems, regularization, level set methods, Navier-Stokes equations

**Credits:** 3

**Instructor:** Jean-Christophe Nave

**Prerequisites:** MATH 315 or MATH 325 or MATH 263; MATH 317 or MATH 387 or COMP 350 or MECH 309; or permission of the instructor

###### MATH 488 - Honours Set Theory - Winter 2019 - Section 001

Axioms of set theory, ordinal and cardinal arithmetic, consequences of the axiom of choice, models of set theory, constructible sets and the continuum hypothesis, introduction to independence proofs.

**Credits:** 3

**Instructor:** Marcin Sabok

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

**Restrictions:** Not open to students who have taken or are taking MATH 590.

###### MATH 517 - Honours Linear Optimization - Fall 2018 - Section 001

Honours level introduction to linear optimization and its applications: duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interiorpoint methods, quadratic optimization, applications in game theory.

**Credits:** 4

**Instructor:** Van Quang Nguyen

**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 417 or MATH 487.

###### MATH 523 - Generalized Linear Models - Winter 2019 - Section 001

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: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.

**Credits:** 4

**Instructor:** Johanna Neslehova

**Prerequisites:** MATH 423

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

###### MATH 524 - Nonparametric Statistics - Fall 2018 - Section 001

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.

**Credits:** 4

**Instructor:** Christian Genest

**Prerequisites:** MATH 324 or equivalent

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

###### MATH 525 - Sampling Theory and Applications - Winter 2019 - Section 001

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

**Instructor:** Russell Steele

**Prerequisites:** MATH 324 or equivalent

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

###### MATH 533 - Honours Regression and Analysis of Variance - Fall 2018 - Section 001

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

**Credits:** 4

**Instructor:** Yi Yang

**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 - Winter 2019 - Section 001

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

**Instructor:** Anmar Khadra

**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 545 - Introduction to Time Series Analysis - Fall 2018 - Section 001

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

**Instructor:** Russell Steele

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

###### MATH 547 - Stochastic Processes - Winter 2019 - Section 001

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:** 4

**Instructor:** TBA

**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 - Winter 2019 - Section 001

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.

**Credits:** 4

**Instructor:** TBA

**Restrictions:** Permission of instructor.

###### MATH 552 - Combinatorial Optimization - Fall 2018 - Section 001

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.

**Credits:** 4

**Instructor:** Bruce Alan Reed

**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 - Fall 2018 - Section 001

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

**Instructor:** Yang Cai

**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 - Winter 2019 - Section 001

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

**Credits:** 4

**Instructor:** Peter Bartello

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

###### MATH 556 - Mathematical Statistics 1 - Fall 2018 - Section 001

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

**Instructor:** Masoud Asgharian-Dastenaei

**Prerequisites:** MATH 357 or equivalent

###### MATH 557 - Mathematical Statistics 2 - Winter 2019 - Section 001

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

**Credits:** 4

**Instructor:** Abbas Khalili Mahmoudabadi

**Prerequisites:** MATH 556

###### MATH 560 - Optimization - Winter 2019 - Section 001

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

**Instructor:** Tim Hoheisel

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

###### MATH 564 - Advanced Real Analysis 1 - Fall 2018 - Section 001

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

**Instructor:** John A Toth

**Prerequisites:** MATH 454, MATH 455 or equivalents

###### MATH 565 - Advanced Real Analysis 2 - Winter 2019 - Section 001

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

**Instructor:** John A Toth

**Prerequisites:** MATH 564

###### MATH 570 - Higher Algebra 1 - Fall 2018 - Section 001

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

**Instructor:** Eyal Z Goren

**Prerequisites:** MATH 457 or equivalent

###### MATH 571 - Higher Algebra 2 - Winter 2019 - Section 001

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

**Instructor:** Henri Darmon

**Prerequisites:** MATH 570 or consent of instructor

###### MATH 576 - Geometry and Topology 1 - Fall 2018 - Section 001

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

**Instructor:** Daniel T. Wise

**Prerequisites:** MATH 454

###### MATH 577 - Geometry and Topology 2 - Winter 2019 - Section 001

Basic properties of differentiable manifolds, tangent and cotangent bundles, differential forms, de Rham cohomology, integration of forms, Riemannian metrics, geodesics, Riemann curvature.

**Credits:** 4

**Instructor:** Niky Kamran

**Prerequisites:** MATH 576

###### MATH 578 - Numerical Analysis 1 - Fall 2018 - Section 001

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

**Instructor:** Adam M. Oberman

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

###### MATH 579 - Numerical Differential Equations - Winter 2019 - Section 001

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.

**Credits:** 4

**Instructor:** Adam M. Oberman

**Prerequisites:** MATH 475 and MATH 387 or permission of the instructor.

###### MATH 580 - Partial Differential Equations 1 - Fall 2018 - Section 001

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

**Instructor:** Gantumur Tsogtgerel

**Prerequisites:** MATH 475 or equivalent

###### MATH 581 - Partial Differential Equations 2 - Winter 2019 - Section 001

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

**Instructor:** Gantumur Tsogtgerel

**Prerequisites:** MATH 455 or equivalent, MATH 580.

###### MATH 582 - Algebraic Topology - Winter 2019 - Section 001

CW-complexes, cellular approximation theorem. Homotopy groups, long exact sequence for a fiber bundle. Whitehead theorem. Freudenthal suspension theorem. Singular and cellular homology and cohomology. Hurewicz theorem. Mayer-Vietoris sequence. Universal coefficients theorem. Cup product, Kunneth formula, Poincare duality.

**Credits:** 4

**Instructor:** Piotr Przytycki

**Prerequisites:** MATH 576 or equivalent or permission of instructor.

###### MATH 587 - Advanced Probability Theory 1 - Fall 2018 - Section 001

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

**Instructor:** Linan Chen

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

###### MATH 589 - Advanced Probability Theory 2 - Winter 2019 - Section 001

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.

**Credits:** 4

**Instructor:** Dana Louis Addario-Berry

**Prerequisites:** MATH 587 or equivalent

###### MATH 590 - Advanced Set Theory - Winter 2019 - Section 001

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

**Credits:** 4

**Instructor:** Marcin Sabok

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

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

###### MATH 635 - Functional Analysis 1 - Fall 2018 - Section 001

Banach spaces. Hilbert spaces and linear operators on these. Spectral theory. Banach algebras. A brief introduction to locally convex spaces.

**Credits:** 4

**Instructor:** Stephen W Drury

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

###### MATH 680 - Computation Intensive Statistics - Fall 2018 - Section 001

General introduction to computational methods in statistics; optimization methods; EM algorithm; random number generation and simulations; bootstrap, jackknife, cross-validation, resampling and permutation; Monte Carlo methods: Markov chain Monte Carlo and sequential Monte Carlo; computation in the R language.

**Credits:** 4

**Instructor:** Yi Yang

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

###### MATH 706 - Advanced Topics in Geometry and Topology 1 - Fall 2018 - Section 001

This course covers an advanced topic in geometry and topology.

**Credits:** 4

**Instructor:** Jacques Claude Hurtubise

###### MATH 706 - Advanced Topics in Geometry and Topology 1 - Winter 2019 - Section 001

This course covers an advanced topic in geometry and topology.

**Credits:** 4

**Instructor:** Gantumur Tsogtgerel

###### MATH 726 - Advanced Topics in Number Theory - Fall 2018 - Section 001

This course covers an advanced topic in number theory.

**Credits:** 4

**Instructor:** Henri Darmon

###### MATH 761 - Advanced Topics in Applied Mathematics 1 - Fall 2018 - Section 001

This course covers an advanced topic in applied mathematics.

**Credits:** 4

**Instructor:** Tim Hoheisel

###### MATH 761 - Advanced Topics in Applied Mathematics 1 - Fall 2018 - Section 002

This course covers an advanced topic in applied mathematics.

**Credits:** 4

**Instructor:** Antony Raymond Humphries

###### MATH 762 - Advanced Topics in Applied Mathematics 2 - Fall 2018 - Section 001

This course covers an advanced topic in applied mathematics.

**Credits:** 4

**Instructor:** Jean-Christophe Nave