Please see below for a list of MATH courses, descriptions and when the course is offered.
MATH 111. Mathematics for Education Students.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Restriction: 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
- Offered by the Faculty of Science. Note: all Science courses have limited enrolment
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MATH 122. Calculus for Management.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Review of functions, exponents and radicals,exponential and logarithm. 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.Trigonometric functions are not discussed in this course.
- Offered by the Faculty of Science. Students intending to pursue the major program or the minor programs offered by the Department of Mathematics and Statistics in the Desautels Faculty of Management should take MATH 140 [or MATH 139] and MATH 141 instead.
- 3 hours lecture, 1 hour tutorial
- Prerequisite: A course in functions.
- Restriction(s): Not open to students who have taken or are taking MATH 139 or MATH 140 or MATH 150 or CEGEP objective 00UN. 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 Desautels Faculty of Management students only.
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MATH 123. Linear Algebra and Probability.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025, Winter 2026
Description
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.
- 3 hours lecture, 1 hour tutorial.
- Restriction(s): Not open to students who have taken or are taking 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 the major program or one of the minor programs offered by the Department of Mathematics and Statistics in the Faculty of Management should take MATH 133 instead.
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MATH 125. Mathematical Techniques for Economics.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Differentation of single and multivarible functions; optimization of single and multivarible functions; constrained optimization of multivariable functions; elements of integration; applications to economics.
- Restriction(s): Not open to students who have taken MATH 122 or MATH 141 or CEGEP objective 00UP or an equivalent CEGEP course covering integral calculus.
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MATH 133. Linear Algebra and Geometry.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases. Linear transformations. Eigenvalues and diagonalization.
- 3 hours lecture, 1 hour tutorial
- Prerequisite: a course in functions
- Restriction(s): 1) Not open to students who have taken CEGEP objective 00UQ or equivalent. 2) Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.
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MATH 139. Calculus 1 with Precalculus.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Review of trigonometry and other Precalculus topics. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
- Fall
- 4 hours lecture, 1 hour tutorial
- Prerequisite: a course in functions
- Restriction: 1) Not open to students who have taken CEGEP objective 00UN or equivalent.2) Not open to students who have taken or are taking MATH 140 or MATH 150. 3) Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics.
- Students continue in MATH 141
- Each Tutorial section is enrolment limited
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MATH 140. Calculus 1.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
- 3 hours lecture, 1 hour tutorial
- Prerequisite: High School Calculus
- Restriction(s): 1) Not open to students who have taken MATH139 or MATH 150 or CEGEP objective 00UN or equivalent. 2) Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematics and Statistics.
- Each Tutorial section is enrolment limited
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MATH 141. Calculus 2.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
- Prerequisites: MATH 139 or MATH 140 or MATH 150.
- Restriction(s): Not open to students who have taken CEGEP objective 00UP or equivalent.
- Restriction(s): Not open to students who have taken or are taking MATH 122,except by permission of the Department of Mathematics and Statistics.
- Each Tutorial section is enrolment limited
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MATH 150. Calculus A.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Functions, limits and continuity, differentiation, L'Hospital's rule, applications, Taylor polynomials, parametric curves, functions of several variables.
- Fall
- 3 hours lecture, 2 hours tutorial
- Students with no prior exposure to vector geometry are advised to take MATH 133 concurrently. Intended for students with high school calculus who have not received six advanced placement credits
- Restriction(s): 1) Not open to students who have taken or are taking MATH 139 or MATH 140 or CEGEP objective 00UN or equivalent. 2) Not open to students who have taken or are taking MATH 122,except by permission of the Department of Mathematics and Statistics.
- MATH 150 and MATH 151 cover the material of MATH 139, MATH 140, MATH 141, MATH 222
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MATH 151. Calculus B.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Integration, methods and applications, infinite sequences and series, power series, arc length and curvature, multiple integration.
- Winter
- 3 hours lecture; 2 hours tutorial
- Each Tutorial section is enrolment limited
- Prerequisite: MATH 150
- Restriction(s): 1) Not open to students who have taken or are taking MATH 141 or CEGEP objective 00UP or equivalent. 2) Not open to students who have taken or are taking MATH 122, except by permission of the Department of Mathematic sand Statistics.
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MATH 180. The Art of Mathematics.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
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MATH 203. Principles of Statistics 1.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
Examples of statistical data and the use of graphical means to summarize the data. Basic distributions arising in the natural and behavioural sciences. The logical meaning of a test of significance and a confidence interval. Tests of significance and confidence intervals in the one and two sample setting (means, variances and proportions).
- No calculus prerequisites
- Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
- You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar. Students should consult http://www.mcgill.ca/students/transfercredit for information regarding transfer credits for this course.
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MATH 204. Principles of Statistics 2.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Prerequisite: MATH 203 or equivalent. No calculus prerequisites
- Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
- You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
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MATH 206. Applied Calculus and Linear Algebra.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Linear algebra in real coordinate space: eigenvalues and diagonalization, applications; orthogonality, Gram-Schmidt process, orthogonal projection; spectral theorem for symmetric matrices; singular value decomposition; positive definite matrices. Multivariable calculus: partial derivatives; linear and quadratic approximation; directional derivatives and gradient; classification of extreme values; constrained optimization. Examples and applications in data science.
- Prerequisites : MATH 133, and MATH 140 or MATH 139, and MATH 141.
- Restrictions: Not open to students who have taken or are taking MATH 222 or MATH 223.
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MATH 208. Introduction to Statistical Computing.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Basic data management. Data visualization. Exploratory data analysis and descriptive statistics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.
- Prerequisite(s): MATH 133
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MATH 209. Fundamentals of Statistical Modeling and Inference.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Introduction to statistical modelling, likelihood principle and maximum likelihood estimation, Bayesian principle and Bayesian estimation, with emphasis on their application in statistical analysis and data science.
- Prerequisites: MATH 203, and MATH 206 and MATH 208, or equivalent
- Restrictions: Not open to students who have received credits for MATH 324.
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MATH 222. Calculus 3.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
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.
- Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
- Restriction: Not open to students who have taken or are taking MATH 150, MATH 151, MATH206, or MATH 262.
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MATH 223. Linear Algebra.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025, Winter 2026
Description
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.
- Fall and Winter
- Prerequisite: MATH 133 or equivalent
- Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 206, MATH 236, MATH 247, or MATH 251.
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MATH 228. Classical Geometry.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Restrictions: Cannot be taken for credit by students in Mathematics and Statistics programs.
- Not open to students who have taken or are taking MATH 348 or MATH 398.
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MATH 235. Algebra 1.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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; homomorphisms and quotient groups.
- Fall
- 3 hours lecture; 1 hour tutorial
- Prerequisite: MATH 133 or equivalent
- Restrictions: Not open to students who have taken or are taking MATH 245.
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MATH 236. Algebra 2.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Prerequisite: MATH 235
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MATH 240. Discrete Structures.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025, Winter 2026
Description
Introduction to discrete mathematics and applications. Logical reasoning and methods of proof. Elementary number theory and cryptography: prime numbers, modular equations, RSA encryption. Combinatorics: basic enumeration, combinatorial methods, recurrence equations. Graph theory: trees, cycles, planar
graphs.
- Fall and Winter
- Corequisite: MATH 133.
- Restriction: 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.
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MATH 242. Analysis 1.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
- Fall
- Prerequisite: MATH 141
- Restriction(s): Not open to students who are taking or who have taken MATH 254.
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MATH 243. Analysis 2.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Prerequisite: MATH 242 or MATH 254.
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MATH 245. Honours Algebra 1.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Honours level: Sets, functions, and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. In-depth study of rings, ideals, and quotient rings; fields and construction of fields from polynomial rings; groups, subgroups, and cosets, homomorphisms, and quotient groups.
- Prerequisites: Prerequisites: MATH 133 or equivalent
- Restrictions: Not open to students who have taken or are taking MATH 235.
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MATH 247. Honours Applied Linear Algebra.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Prerequisite: MATH 133 or equivalent.
- Restriction: Intended for Honours Physics and Engineering students
- Restriction: Not open to students who have taken or are taking MATH 236, MATH 223 or MATH 251
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MATH 248. Honours Vector Calculus.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Partial derivatives and differentiation of functions in several variables; Jacobians;
maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
- Fall and Winter and Summer
- Prerequisites: MATH 133 and MATH 222 or consent of Department.
- Restriction: Intended for Honours Physics, Computer Science, Physiology and Engineering students.
- Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358.
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MATH 249. Honours Complex Variables.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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. Additional topics if time permits: homotopy of paths and simple connectivity, Riemann sphere, rudiments of analytic continuation.
- Winter
- Prerequisite(s): MATH 222
- Restriction: Intended for Honours Physics and Engineering students
- Restriction: Not open to students who have taken or are taking MATH 316
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MATH 251. Honours Algebra 2.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Prerequisites: MATH 235 or permission of the Department
- Restriction: Not open to students who are taking or have taken MATH 247
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MATH 254. Honours Analysis 1.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Prerequisite(s): MATH 141
- Restriction(s): Not open to students who are taking or who have taken MATH 242.
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MATH 255. Honours Analysis 2.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Hölder 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.
- Winter
- Prerequisites: MATH 242 or MATH 254 or permission of the Department
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MATH 262. Intermediate Calculus.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Engineering)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
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.
- (3-1-5)
- 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.
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MATH 263. Ordinary Differential Equations for Engineers.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Engineering)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
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.
- (3-1-5)
- Corequisite: 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.
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MATH 264. Advanced Calculus for Engineers.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Engineering)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
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.
- (3-1-5)
- Prerequisite: MATH 262 or MATH 151 or MATH 152 or equivalent.
- Corequisite: 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.
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MATH 271. Linear Algebra and Partial Differential Equations.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Engineering)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Applied Linear Algebra. Linear Systems of Ordinary Differential Equations. Power Series Solutions. Partial Differential Equations. Sturm-Liouville Theory and Applications. Fourier Transforms.
- Fall and Winter
- (3-1-5)
- Prerequisites: MATH 263, MATH 264.
- Not open to students who have taken MATH 266.
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MATH 308. Fundamentals of Statistical Learning.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Theory and application of various techniques for the exploration and analysis of multivariate data: principal component analysis, correspondence analysis, and other visualization and dimensionality reduction techniques; supervised and unsupervised learning; linear discriminant analysis, and clustering techniques. Data applications using appropriate software.
- Prerequisite(s): MATH 208, one of MATH 223, MATH 236, MATH 247, MATH 251; MATH 323 or MATH 356.
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MATH 314. Advanced Calculus.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025, Winter 2026
Description
Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
- Prerequisites: MATH 133, MATH 222
- Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358.
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MATH 315. Ordinary Differential Equations.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025, Winter 2026
Description
First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
- Prerequisite: MATH 222.
- Corequisite: MATH 133.
- Restriction: Not open to students who have taken or are taking MATH 325.
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MATH 316. Complex Variables.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Algebra of complex numbers, Cauchy-Riemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
- Fall
- Prerequisites: MATH 314 or equivalent and MATH 243.
- Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.
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MATH 317. Numerical Analysis.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
- 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
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MATH 318. Mathematical Logic.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisite(s): MATH 235 or MATH 240 or MATH 242.
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MATH 319. Partial Differential
Equations
.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.
- Winter
- Prerequisites: MATH 223 or MATH 236, MATH 314 or equivalent, MATH 315
- Not open to students who have taken or are taking MATH 475.
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MATH 323. Probability.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
- Prerequisites: MATH 141 or equivalent.
- Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
- Restriction: Not open to students who have taken or are taking MATH 356
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MATH 324. Statistics.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025, Winter 2026
Description
Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
- Fall and Winter
- Prerequisite: MATH 323 or equivalent
- Restriction: Not open to students who have taken or are taking MATH 357
- You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
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MATH 325. Honours Ordinary Differential Equations.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
- Fall and Winter
- (3-0-6)
- Prerequisite: MATH 222.
- Restriction: Intended for Honours Mathematics, Physics and Engineering programs.
- Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315
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MATH 326. Nonlinear Dynamics and Chaos.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisites: MATH 222, MATH 223
- Restriction: Not open to students who have taken or are taking MATH 376
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MATH 327. Matrix Numerical Analysis.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
- Winter
- Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.
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MATH 329. Theory of Interest.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
- Winter
- Prerequisite: MATH 141
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MATH 335. Groups, Tilings and Algorithms.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Transformation groups of the plane. Inversions and Moebius transformations. The hyperbolic plane. Tilings in dimension 2 and 3. Group presentations and Cayley graphs. Free groups and Schreier's theorem. Coxeter groups. Dehn's Word and Conjugacy Problems. Undecidability of the Word Problem for semigroups. Regular
languages and automatic groups. Automaticity of Coxeter groups.
- Prerequisites: MATH 235
- Restriction(s): Not open to students who have taken or are taking MATH 365.
- Note: This course is intended primarily for students in the Major Program in Mathematics and the Joint Major Program in Mathematics and Computer Science.
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MATH 338. History and Philosophy of Mathematics.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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, culminating in the discovery of the infinitesimal and integral calculus by Newton and Leibnitz. Demonstration of how mathematics was done in past centuries, and involves the practice of mathematics, including detailed calculations, arguments based on geometric reasoning, and proofs.
- Fall
- Prerequisites: MATH 133, MATH 141.
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MATH 340. Discrete
Mathematics.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
- Winter
- Prerequisites: MATH 235 or MATH 240 or MATH 242.
- Corequisites: MATH 223 or MATH 236.
- Restriction: Restriction: Not open to students who have taken or are taking MATH 350.
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MATH 346. Number Theory.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
- Winter
- Prerequisite: MATH 235 or consent of instructor
- Restriction: Not open to students who have taken or are taking MATH 377.
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MATH 348. Euclidean Geometry.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Prerequisite: MATH 133 or equivalent or permission of instructor.
- Restriction: Not open to students who have taken MATH 398.
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MATH 350. Honours Discrete Mathematics
.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.
- Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.
- Restrictions: Not open to students who have taken or are taking MATH 340. Intended for students in mathematics or computer science honours programs.
- Intended for students in mathematics or computer science honours programs.
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MATH 352. Problem Seminar.
Credits: 1
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.
- Prerequisite: Enrolment in a math related program or permission of the instructor.
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MATH 356. Honours Probability.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisite(s): MATH 243 or MATH 255, and MATH 222 or permission of the Department.
- Restriction: Not open to students who have taken or are taking MATH 323
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MATH 357. Honours Statistics.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Sampling distributions. Point estimation. Minimum variance unbiased estimators,
sufficiency, and completeness. Confidence intervals. Hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests. Likelihood ratio tests for normal samples. Asymptotic sampling distributions and inference.
- Winter
- Prerequisite: MATH 356 or equivalent
- Restriction: Not open to students who have taken or are taking MATH 324
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MATH 358. Honours Advanced Calculus.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Point-set topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.
- Prerequisites: MATH 222, MATH 247 or MATH 251, MATH 255 or permission of the Department.
- Restrictions: Intended for students in Honours Mathematics programs, Not open to students who have taken or are taking MATH 314 or MATH 248
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MATH 365. Honours Groups, Tilings and Algorithms.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Transformation groups of the plane. Inversions and Moebius transformations. The hyperbolic plane. Tilings in dimension 2 and 3. Group presentations and Cayley graphs. Free groups and Schreier's theorem. Coxeter groups. Dehn's Word and Conjugacy Problems. Undecidability of the Word Problem for semigroups. Regular languages and automatic groups. Automaticity of Coxeter groups.
- Prerequisite: MATH 235
- Restrictions: Not open to students who have taken or are taking MATH 335.
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MATH 376. Honours Nonlinear Dynamics.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
This course consists of the lectures of
MATH 326, but will be assessed at the honours level.
- Fall
- Prerequisites: MATH 222, MATH 223
- Restrictions: Intended primarily for Honours students. Not open to students who have taken or are taking MATH 326.
- Note: Additionally, a special project or projects may be assigned.
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MATH 377. Honours Number Theory.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
This course consists of the lectures of
MATH 346, but will be assessed at the honours level.
- Winter
- Prerequisite: Enrolment in Mathematics Honours program or consent of instructor
- Restriction: Not open to students who have taken or are taking MATH 346.
- Note: Additionally, a special project or projects may be assigned.
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MATH 378. Nonlinear Optimization
.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Optimization terminology. Convexity. First- and second-order optimality conditions for unconstrained problems. Numerical methods for unconstrained optimization:
Gradient methods, Newton-type methods, conjugate gradient methods, trust-region methods. Least squares problems (linear + nonlinear). Optimality conditions for smooth constrained optimization problems (KKT theory). Lagrangian duality. Augmented Lagrangian methods. Active-set method for quadratic programming. SQP methods.
- Prerequisites: MATH 223 or MATH 247 or MATH 236 or MATH 251. MATH 248 or MATH 314 or MATH 358. MATH 243 or MATH 255.
- Not open to students who have taken MATH 560.
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MATH 387. Honours Numerical Analysis.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
- Taught in alternate years
- Winter (even years)
- Prerequisites: MATH 325 or MATH 315, COMP 202 or permission of instructor.
- Corequisites: MATH 255 or MATH 243.
- Restriction: Intended primarily for Honours students.
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MATH 396. Undergraduate Research Project.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Independent research project with a final written report.
- 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.
- Note: Enrolment may be limited. Students are advised to start the application process well before the start of the term and to plan for an alternative course in the case that no suitable project is available. Individual projects may be suggested each term which may have project-specific prerequisites. Students may also approach professors to devise their own projects. Some projects may be accessible to students in other disciplines. See https://www.mcgill.ca/science/research/undergraduate-research/science-re... for more information about available projects and application forms and procedures.
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MATH 397. Honours Matrix Numerical Analysis.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Winter
- Prerequisites: MATH 251 or MATH 247, COMP 202 or permission of the instructor.
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MATH 398. Honours Euclidean Geometry
.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Prerequisite: MATH 133 or equivalent or permission of instructor.
- Restrictions: Not open to students taking or have take MATH 348.
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[course medium MATH ]
MATH 410. Majors Project.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
A supervised project.
- Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
- Requires departmental approval.
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MATH 417. Linear Optimization.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent
- Restriction: Not open to students who have taken or are taking MATH 487 or MATH 517.
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MATH 420. Independent Study.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
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.
- Fall and Winter and Summer
- Requires approval by the chair before registration
- Please see regulations concerning Project Courses under Faculty Degree Requirements
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MATH 423. Applied Regression.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Multiple regression estimators and their properties. Hypothesis tests and confidence
intervals. Analysis of variance. Prediction and prediction intervals. Model diagnostics. Model selection. Introduction to weighted least squares. Basic contingency table analysis. Introduction to logistic and Poisson regression. Applications to experimental and observational data.
- Fall
- Prerequisites: (MATH 209 or MATH 324) and (MATH 206 or MATH 223 or MATH 236)
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MATH 427. Statistical Quality Control.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
- Prerequisites: MATH 203 or equivalent, and MATH 204 or MATH 324.
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MATH 430. Mathematical Finance.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Prerequisite(s): MATH 243 or MATH 255, and MATH 323 or MATH 356, and MATH 133 or equivalent.
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MATH 437. Mathematical Methods in Biology.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- This course is offered in the winter semester.
- Prerequisite(s): MATH 315 or MATH 325, and MATH 326 or MATH 376, and COMP 202 or COMP 204 or COMP 208 or equivalent.
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MATH 447. Introduction to Stochastic Processes.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Prerequisite: MATH 323
- Restriction: Not open to students who have taken or are taking MATH 547.
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MATH 451. Introduction to General
Topology.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
This course is an introduction to point set topology. Topics include basic set theory and logic, topological spaces, separation axioms, continuity, connectedness,
compactness, Tychonoff Theorem, metric spaces, and Baire spaces.
- Prerequisites: MATH 242 or MATH 254
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MATH 454. Honours Analysis 3.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov’s theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus.
- Prerequisite(s): MATH 255
- Restriction: Not open to students who have taken MATH 354.
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MATH 455. Honours Analysis 4.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval’s identity, Poisson summation formula.
- Prerequisite: MATH 454 or equivalent.
- Restriction(s): Not open to students who have taken MATH 355.
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MATH 456. Honours Algebra 3.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Groups, quotient groups and the isomorphism theorems. Group actions. Groups of prime order and the class equation. Sylow's theorems. Simplicity of the alternating group. Semidirect products. Principal ideal domains and unique factorization domains. Modules over a ring. Finitely generated modules over a principal ideal domain with applications to canonical forms.
- Prerequisites: MATH 235 or MATH 245
- Restriction: Not open to students who have taken MATH 370.
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MATH 457. Honours Algebra 4.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Representations of finite groups. Maschke's theorem. Schur's lemma. Characters, their orthogonality, and character tables. Field extensions. Finite and cyclotomic fields. Galois extensions and Galois groups. The fundamental theorem of Galois theory. Solvability by radicals.
- Prerequisite: (MATH 236 or MATH 251) and MATH 456
- Restriction(s): Not open to students who have taken MATH 371.
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MATH 458. Honours Differential Geometry.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
In addition to the topics of
MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.
- Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314 or MATH 358
- Restriction: Not open to students who have taken MATH 380.
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MATH 462. Machine Learning
.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Introduction to supervised learning: decision trees, nearest neighbors, linear models, neural networks. Probabilistic learning: logistic regression, Bayesian methods, naive Bayes. Classification with linear models and convex losses. Unsupervised learning: PCA, k-means, encoders, and decoders. Statistical learning theory: PAC learning and VC dimension. Training models with gradient descent and stochastic gradient descent. Deep neural networks. Selected topics chosen from: generative models, feature representation learning, computer vision.
- Prerequisites: (MATH 236 or MATH 247 or MATH 251) and (MATH 248 or MATH 314 or MATH 358) and (COMP 202 or equivalent or permission of the instructor).
- Restriction: Not open to students who have taken or are taking COMP 451 or COMP 551.
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MATH 463. Convex Optimization.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal calculus.
Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems, image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed
sensing.
- Prerequisites: MATH 223 or MATH 247 or MATH 236 or MATH 251. MATH 248 or MATH 314 or MATH 358. MATH 243 or MATH 255. COMP 202 or COMP 204 or COMP 208 or equivalent.
- Restriction: Not open to students who have taken or are taking MATH 563.
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MATH 466. Honours Complex Analysis.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.
- Prerequisite: MATH 255.
- Restriction: Not open to students who have taken or are taking MATH 366, MATH 249, MATH 316 and MATH 381.
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MATH 470. Honours Research Project.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
The project will contain a significant research component that requires substantial independent work consisting of a written report and oral examination or presentation.
- Fall and Winter and Summer
- Requires Departmental Approval
- Students are advised to start contacting potential project supervisors early during their U2 year.
- Prerequisite: appropriate honours courses with approval of the project supervisor
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MATH 475. Honours Partial Differential Equations.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
- Prerequisites: MATH 247 or MATH 251 or equivalent, and MATH 248 or MATH 358 or equivalent, MATH 325.
- Restriction: Not open to students who have taken or are taking MATH 319.
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MATH 478. Computational Methods in Applied Mathematics
.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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
- Prerequisites: MATH 315 or MATH 325 or MATH 263; MATH 317 or MATH 387 or COMP 350 or MECH 309; or permission of the instructor
- This course will be taught in the winter semester.
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MATH 480. Honours Independent Study.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Summer 2025, Fall 2025, Winter 2026
Description
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.
- Fall and Winter and Summer
- Please see regulations concerning Project Courses under Faculty Degree Requirements
- Requires approval by the chair before registration
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MATH 488. Honours Set Theory.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Fall
- Prerequisites: MATH 251 or MATH 255 or permission of instructor
- Restrictions :Not open to students who have taken or are taking MATH 590.
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MATH 510. Quantitative Risk Management.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Basics concepts in quantitative risk management: types of financial risk, loss distribution, risk measures, regulatory framework. Empirical properties of financial data, models for stochastic volatility. Extreme-value theory models for maxima and threshold exceedances. Multivariate models, copulas, and dependence measures. Risk aggregation.
- Prerequisites: (MATH 323 or MATH 356 or equivalent) and (MATH 324 or MATH 357 or equivalent)
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MATH 511. Analysis of Categorical
Data.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Probability distributions for categorical data, Analysis of 2X2 contingency tables, Multiway contingency tables, The Logistic regression, Logistic regression for categorical predictors, Logit models for nominal and ordinal responses, Log-linear models and modelling ordinal associations in contingency tables, Unsupervised learning techniques for categorical data, Non Linear Principal component analysis, Applications of unsupervised learning techniques using R, Item Response Theory,
Rasch model. Some topics may be included or excluded as the time permits.
- Prerequisites: (MATH 208 or equivalent) and (MATH 324 or MATH 357) and (MATH 423 or MATH 533 or equivalent).
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MATH 517. Honours Linear Optimization.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- 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.
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MATH 518. Introduction to Algebraic Geometry.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Affine varieties. Radical ideals and Hilbert's Nullstellensatz. The Zariski topology. Irreducible decomposition. Dimension. Tangent spaces, smoothness and singularities. Projective spaces and projective varieties. Regular functions and morphisms. Rational maps and indeterminacy. Blowing up. Divisors and linear systems. Projective curves.
- Prerequisites: MATH 456 or permission of the instructor.
- 1. Some familiarity with rings, ideals, and multivariable calculus is expected.
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MATH 523. Generalized Linear Models.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Exponential families, link functions. Inference and parameter estimation for generalized linear models; model selection using analysis of deviance. Residuals. Contingency table analysis, logistic regression, multinomial regression, Poisson regression, log-linear models. Multinomial models. Overdispersion and Quasilikelihood.
Applications to experimental and observational data.
- Winter
- Prerequisite: MATH 423 or MATH 533 or EPIB 697.
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MATH 524. Nonparametric Statistics.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisite: MATH 324 or equivalent
- Restriction: Not open to students who have taken MATH 424
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MATH 525. Sampling Theory and Applications.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
- Prerequisite: MATH 324 or equivalent
- Restriction: Not open to students who have taken MATH 425
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MATH 527D1. Statistical Data Science
Practicum.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
The holistic skills required for doing statistical data science in practice. Data science life cycle from a statistics-centric perspective and from the perspective of a statistician working in the larger data science environment. Group-based projects with industry, government, or university partners. Statistical collaboration and consulting conducted in coordination with the Data Science Solutions Hub (DaS^2H) of the Computational and Data Systems Initiative (CDSI).
- Prerequisites: MATH 324; MATH 223 ; MATH 208
- Corequisites: MATH 423
- No credit will be given for this course unless both MATH 527D1 and MATH527D2 are successfully completed in consecutive terms.
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MATH 527D2. Statistical Data Science
Practicum.
Credits: 3
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
- Prerequisites: MATH 324; MATH 223 ; MATH 208
- Corequisites: MATH 423
- No credit will be given for this course unless both MATH 527D1 and MATH 527D2 are successfully completed in consecutive terms
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MATH 533. Regression and Analysis of Variance.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Multivariate normal and chi-squared distributions; quadratic forms. Multiple linear
regression estimators and their properties. General linear hypothesis tests. Prediction and confidence intervals. Asymptotic properties of least squares estimators. Weighted least squares. Variable selection and regularization. Selected advanced topics in regression. Applications to experimental and observational
data.
- Prerequisites: MATH 357, MATH 247 or MATH 251.
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MATH 537. Honours Mathematical Models in Biology.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Prerequisite(s): MATH 325, MATH 376, and COMP 202 or COMP 204 or COMP 208 or equivalent.
- Restriction(s): Not open to students who have taken MATH 437.
- This course is offered in the winter semester.
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MATH 545. Introduction to Time Series Analysis.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Prerequisite: MATH 324 or MATH 357 or equivalent
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MATH 547. Stochastic Processes.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains:transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
- Prerequisites: MATH 356 and either MATH 247 or MATH 251.
- Restriction: Not open to students who have taken or are taking MATH 447.
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MATH 550. Combinatorics.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Intended primarily for honours and graduate students in mathematics.
- Restriction: Permission of instructor.
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MATH 552. Combinatorial Optimization.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Algorithmic and structural approaches in combinatorial optimization with a focus upon theory and applications. Topics include: polyhedral methods, network optimization, the ellipsoid method, graph algorithms, matroid theory and submodular functions.
- Prerequisite: MATH 350 or COMP 362 (or equivalent).
- Restriction: Not open to students who have taken or are taking COMP 552.
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MATH 553. Algorithmic Game Theory.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Foundations of game theory. Computation aspects of equilibria. Theory of auctions and modern auction design. General equilibrium theory and welfare economics. Algorithmic mechanism design. Dynamic games.
- Prerequisite: COMP 362 or MATH 350 or MATH 454 or MATH 487, or instructor permission.
- Restriction: Not open to students who are taking or have taken COMP 553
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MATH 555. Fluid Dynamics.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Kinematics. Dynamics of general fluids. Inviscid fluids, Navier-Stokes equations. Exact solutions of Navier-Stokes equations. Low and high Reynolds number flow.
- Fall
- Prerequisite (Undergraduate): MATH 315 and MATH 319 or equivalent
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MATH 556. Mathematical Statistics 1.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisite: MATH 323, MATH 356, or equivalent
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MATH 557. Mathematical Statistics 2.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Sufficiency, minimal and complete sufficiency, ancillarity. Fisher and Kullback-Leibler
information. Elements of decision theory. Theory of estimation and hypothesis testing from the Bayesian and frequentist perspective. Elements of asymptotic statistics including large-sample behaviour of maximum likelihood estimators, likelihood-ratio tests, and chi-squared goodness-of-fit tests.
- Winter
- Prerequisite: MATH 556 and either MATH 324, MATH 357 or equivalent
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MATH 558. Design of Experiments.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Introduction to concepts in statistically designed experiments. Randomization and replication. Completely randomized designs. Simple linear model and analysis of
variance. Introduction to blocking. Orthogonal block designs. Models and analysis for block designs. Factorial designs and their analysis. Row-column designs. Latin squares. Model and analysis for fixed row and column effects. Split-plot designs, model and analysis. Relations and operations on factors. Orthogonal factors. Orthogonal decomposition. Orthogonal plot structures. Hasse diagrams. Applications to real data and ethical issues.
- Prerequisites: MATH 223, MATH 236, MATH 247, MATH 251, or equivalent. MATH 208 or equivalent. MATH 324, MATH 357, or equivalent.
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MATH 559. Bayesian Theory and Methods.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Subjective probability, Bayesian statistical inference and decision making, de Finetti’s representation. Bayesian parametric methods, optimal decisions, conjugate
models, methods of prior specification and elicitation, approximation methods. Hierarchical models. Computational approaches to inference, Markov chain
Monte Carlo methods, Metropolis—Hastings. Nonparametric Bayesian inference.
- Prerequisite: MATH 324, MATH 357, MATH 557, or equivalent, and MATH 208 or equivalent.
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MATH 562. Theory of Machine Learning.
Credits: 0-4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Concentration inequalities, PAC model, VC dimension, Rademacher complexity, convex optimization, gradient descent, boosting, kernels, support vector machines, regression and learning bounds. Further topics selected from: Gaussian processes, online learning, regret bounds, basic neural network theory.
- Prerequisites: MATH 462 or COMP 451 or (COMP 551, MATH 222, MATH 223 and MATH 324) or ECSE 551.
- Restrictions: Not open to students who have taken or are taking COMP 562. Not open to students who have taken COMP 599 when the topic was "Statistical Learning Theory" or "Mathematical Topics for Machine Learning". Not open to students who have taken COMP 598 when the topic was"Mathematical Foundations of Machine Learning".
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MATH 563. Honours Convex Optimization
.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Honours level introduction to convex analysis and convex optimization: Convex sets and functions, subdifferential calculus, conjugate functions, Fenchel duality, proximal
calculus. Subgradient methods, proximal-based methods. Conditional gradient method, ADMM. Applications including data classification, network-flow problems,
image processing, convex feasibility problems, DC optimization, sparse optimization, and compressed sensing.
- Prerequisites: MATH 223 or MATH 247 or MATH 236 or MATH 251. MATH 248 or MATH 314 or MATH 358. MATH 243 or MATH 255. COMP 202 or COMP 204 or COMP 208 or equivalent.
- Restriction: Not open to students who have taken or are taking MATH 463.
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MATH 564. Real Analysis and Measure Theory.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Abstract theory of measure and integration: Borel-Cantelli lemmas, regularity of measures, product measures, Fubini-Tonelli theorem, signed measures, Hahn and Jordan decompositions, Radon-Nikodym theorem, differentiation in R^n.
- Fall
- Prerequisite(s): MATH 255
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MATH 565. Functional Analysis.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Review of the basic theory of Banach and Hilbert spaces, L^p spaces, open mapping theorem,closed graph theorem, Banach-Steinhaus theorem, Hahn-Banach theorem, weak and weak-* convergence, weak convergence of measures, Riesz representation theorems, spectral theorem for compact self-adjoint operators, Fredholm theory, spectral theorem for bounded self-adjoint operators, Fourier series and integrals, additional topics.
- Winter
- Prerequisite(s): MATH 454 or MATH 564.
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MATH 566. Advanced Complex Analysis and Riemann Surfaces
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Brief review of holomorphicity and contour integration. Analytic continuation and the monodromy theorem, normal families. Riemann surfaces; elliptic functions; Picard theorem. Riemann zeta function and prime number theorem. Relations with harmonic analysis; the uniformization theorem. Time permitting, additional material such as: Hodge decomposition, divisors, the Riemann Roch formula, or rudiments of moduli spaces.
- Fall
- Prerequisites: MATH 249 and MATH 455
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MATH 570. Higher Algebra 1.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
Free groups and free products of groups. Categories and functors. Universal properties and adjoint functors. Limits. Introduction to commutative algebra. Tensor products. Localization. Noetherian rings and Hilbert’s basis theorem. Hilbert's Nullstellensatz.
- Fall
- Prerequisite: MATH 456 or permission of the instructor.
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MATH 571. Higher Algebra 2.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Flat, projective, and injective modules. Introduction to homological algebra. Ext and Tor. Group cohomology. Semi-simple rings and modules. The Artin-Wedderburn Theorem.
- Winter
- Prerequisites: MATH 570 or permission of the instructor.
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MATH 574. Dynamical Systems.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Dynamical systems, phase space, limit sets. Review of linear systems. Stability. Liapunov functions. Stable manifold and Hartman-Grobman theorems. Local bifurcations, Hopf bifurcations, global bifurcations. Poincare Sections. Quadratic maps: chaos, symbolic dynamics, topological conjugacy. Sarkovskii's theorem, periodic doubling route to chaos. Smale Horseshoe.
- Winter
- Prerequisites: MATH 325 and MATH 454 or permission of the instructor.
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MATH 576. Geometry and Topology 1.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisite: MATH 454
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MATH 577. Geometry and Topology 2.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Basic properties of differentiable manifolds, tangent and cotangent bundles, differential forms, de Rham cohomology, integration of forms, Riemannian metrics, geodesics, Riemann curvature.
- Winter
- Prerequisite: MATH 576
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MATH 578. Numerical Analysis 1.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisites: MATH 247 or MATH 251; and MATH 387; or permission of the instructor.
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MATH 579. Numerical Differential Equations.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Winter
- Prerequisites: MATH 475 and MATH 387 or permission of the instructor.
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MATH 580. Advanced Partial Differential Equations 1
.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisites: MATH 475 or equivalent
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MATH 581. Advanced Partial Differential Equations 2
.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Winter
- Prerequisite(s): MATH 455 or equivalent, MATH 580.
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MATH 582. Algebraic Topology.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Prerequisite: MATH 576 or equivalent or permission of instructor.
- Course to be taught alternate years - Winter Semester
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MATH 583. Geometric Group Theory.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Actions on trees. Cayley graphs. The word problem. Hyperbolic groups. Quasi-isometry invariants.
- Prerequisite(s): MATH 456 and MATH 576 or equivalent or permission of instructor.
- Course offered alternate years in Fall.
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MATH 587. Advanced Probability Theory 1.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025
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Fall 2025 in Visual Schedule Builder.
Description
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.
- Fall
- Prerequisite(s): MATH 356 and MATH 255 or MATH 243 or equivalent.
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MATH 589. Advanced Probability Theory 2.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
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.
- Winter
- Prerequisites: MATH 587 or equivalent
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MATH 590. Advanced Set Theory.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
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.
- Prerequisites: MATH 251 or MATH 255 or permission of instructor.
- Restriction: Not open to students who have taken or are taking MATH 488.
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MATH 591. Model Theory
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
Structures, theories, and definable sets; elementary equivalence and elementary embeddings; compactness and Löwenheim– Skolem theorems; types, the omitting types theorem, and saturation; categoricity and the Ryll-Nardzewski theorem; quantifier elimination and applications to algebra; ultraproducts; homogeneous structures and Fraïssé theory; infinitary logics. Optional topics: indiscernibles and Morley's theorem; stability; o-minimality; elimination of imaginaries.
- Winter
- Prerequisites: MATH 318 or MATH 488 or MATH 456 or permission of the instructor.
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MATH 592. Descriptive Set Theory
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
Polish spaces; universality of the Hilbert cube, the Cantor space, and the Baire space; the Cantor–Bendixson theorem; Baire spaces; the Borel hierarchy; change of topology techniques; infinite games; analytic and co-analytic sets; analytic separation; the Luzin–Souslin theorem; the Borel and measure isomorphism theorems; regularity properties of analytic sets; uniformization; the projective hierarchy. Optional topics: Polish groups and their actions; definable equivalence relations and graphs; effective descriptive set theory.
- Winter
- Prerequisites: MATH 454 or MATH 451 or permission of the instructor.
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MATH 594. Topics in Mathematics and Statistics
.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
This course covers a topic in mathematics and/or statistics.
- Prerequisites: At least 30 credits in required or complementary courses from the Honours Mathematics, Honours Applied Mathematics, or Honours Probability and Statistics programs. 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
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MATH 595. Topics in Analysis.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
This course covers a topic in analysis.
- Prerequisite(s):At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 454 or MATH 366 or MATH 466. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restriction: Requires permission of the Department of Mathematics and Statistics.
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MATH 596. Topics in Algebra and Number Theory.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
This course covers a topic in algebra and/or number theory.
- Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 456 or MATH 377. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restriction(s): Requires permission of the Department of Mathematics and Statistics.
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MATH 597. Topics in Applied Mathematics.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
This course covers a topic in applied mathematics.
- Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Applied Mathematics program. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restriction(s): Requires permission of the Department of Mathematics and Statistics.
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MATH 597. Topics in Applied Mathematics.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
This course is not offered this catalogue year.
Description
This course covers a topic in applied mathematics.
- Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Applied Mathematics program. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restriction(s): Requires permission of the Department of Mathematics and Statistics.
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MATH 598. Topics in Probability & Statistics
Credits: 0-4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Fall 2025, Winter 2026
Description
This course covers a topic in probability and/or statistics.
- Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Probability and Statistics program including MATH 356. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restriction(s): Requires permission of the Department of Mathematics and Statistics.
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MATH 599. Topics in Geometry and Topology.
Credits: 4
Offered by: Mathematics and Statistics (Faculty of Science)
Terms offered: Winter 2026
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Winter 2026 in Visual Schedule Builder.
Description
This course covers a topic in geometry and/or topology.
- Prerequisites: At least 30 credits in required or complementary courses from the Honours in Mathematics program including MATH 454 and MATH 458. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
- Restriction(s): Requires permission of the Department of Mathematics and Statistics.
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