Courses

Mathematics and mathematical thinking for prospective elementary school teachers. Number systems and counting, symmetry and patterns, graphs and networks, with examples from nature and art. Excludes any MATH course, or its equivalent, which counts toward a major or minor in Mathematics. Does not satisfy the Mathematics requirement for a Bachelor of Science degree. Excludes MATH-EDUC 2080Y.

Cross-listed: EDUC-2081H

Mathematics and mathematical thinking for prospective elementary school teachers. Measurement and growth, probability, and statistics, with examples from nature and art. Excludes any MATH course, or its equivalent, which counts toward a major or minor in Mathematics. Excludes MATH-EDUC 2080Y. Does not satisfy the Mathematics requirement for a Bachelor of Science degree.

Cross-listed: EDUC-2082H

Multivariable functions, curves, and surfaces in two and three dimensions. Partial differentiation and applications. Multiple integrals. Prerequisite: 60% or higher in MATH 1350H and in one of 1120H or 1100Y or 1101Y.

Parametric curves and surfaces, vector functions and fields. Line integrals, Green's Theorem. Surface integrals, curl and divergence, Stokes' and Divergence Theorems. Introduction to Fourier methods and complex numbers. Prerequisite: MATH 2110H.

Analytical and computational methods for obtaining the motion of simple physical systems. Includes motion in one dimension, projectile motion, realistic motion of objects with drag and spin, oscillatory motion, chaos in the nonlinear pendulum. Students use a mix of analytical calculus-based methods and scientific computing tools to solve problems. Prerequisite: 60% or higher in PHYS 1001H and MATH 1120H. Pre- or co-requisite: MATH 2150H. Strongly recommended: COIS 1020H. Excludes PHYS 2110H, PHYS-COIS 2310H, PHYS-MATH 3130H.

Cross-listed: PHYS-2130H

First order equations; qualitative and numerical methods. Second order linear equations. Linear systems. Applications to physical and biological models. Laplace transforms. Prerequisite: 60% or higher in MATH 1120H or 1100Y or 1101Y. Recommended: MATH 1350H.

Cross-listed: PHYS-2150H

Introduces concepts and methods that are essential for all advanced courses in pure mathematics. Intended for Mathematics majors early in their program. Introduction to logic, abstraction, and proof through exploration of sets, elementary topology of Euclidean spaces, sequences and series of number and functions, integers, polynomials, and modular arithmetic. Prerequisite: MATH 1120H and 1350H.

Elements of Euclidean geometry, stressing its axiomatic development. Recommended for Education students. Prerequisite: One of MATH 1005H, 1110H, or 1350H.

Complex numbers, vector spaces, basis and dimension, linear transformations, diagonalization, quadratic forms, least squares, inner product spaces, orthogonality, Fourier series. Prerequisite: MATH 1110H (or 1100Y or 1101Y) and 1350H.

An introduction to applied statistical theory and methods. Probability distributions and the central limit theorem, methods of point estimation, confidence intervals, hypothesis testing, comparative inferences, and nonparametric methods. Computer methods in statistics. Prerequisite: MATH 1550H and one of MATH 1005H or 1110H.

Intermediate probability theory as a basis for further study in mathematical statistics and advanced probability, including stochastic processes. Random variables, jointly distributed random variables, transformations and generating functions, conditioning and conditional expectation. Binomial, Poisson, Exponential, Gamma, and Normal distributions. Prerequisite: MATH 1550H, and one of MATH 1005H or 1110H. Excludes MATH 3570H.

Mathematics related to computer science, including sets and relations, counting techniques and recursive relations, trees and networks. Applications to analysis of algorithms, data structure, and optimization problems. Prerequisite: MATH 1350H and 1120H; or COIS 1020H, MATH 1350H, and one of MATH 1005H or 1110H.

Cross-listed: COIS-2600H

Classical mechanics of particles in three dimensions. Topics include motion in non-inertial reference frames, gravity, central forces, and special relativity. Prerequisite: PHYS-MATH 2130H (or PHYS 2110H). Pre- or co-requisite: MATH 2110H and 2150H.

Cross-listed: PHYS-3130H

The transport equation, heat equation, wave equation, Laplace equation, Poisson equation, in one, two, and three dimensions, in Cartesian, Polar, and/or Spherical coordinates. Physical interpretations. Properties of harmonic functions. Fourier theory: uniform, pointwise, and L2 convergence. Initial/boundary value problems: existence and uniqueness of solutions. Solutions to I/BVPs using orthogonal eigenfunction expansions. Solutions to I/BVPs using convolutional transforms. Prerequisite: MATH 2150H and 2170H. Strongly recommended: MATH 1350H.

Cross-listed: PHYS-3150H

Differential equations in applied mathematics, including Bessel, Legendre, hypergeometric, Laguerre, Hermite, Chebyshev, etc. Series and numerical solutions. Properties of the special functions arising from these equations. Prerequisite: 60% or higher in MATH-PHYS 2150H. Recommended: MATH 2200H.

Cross-listed: PHYS-3160H

Divisibility (GCDs, LCMs, Euclidean algorithm, Bezout's identity). Linear Diophantine Equations. Prime numbers (Factorization; Fermat/Mersenne numbers; pseudoprimes; Carmichael numbers). Modular Arithmetic (Chinese Remainder Theorem; Fermat/ Euler theorem). Group of units mod m. Primitive roots. Quadratic Residues (Legendre symbols; Quadratic Reciprocity). Prerequisite: MATH 1350H and 2200H.

An introduction to the fundamental algebraic structures: groups, rings, fields. Subgroups and subrings, homomorphisms and isomorphisms, quotient structures, finite fields. Selected applications. Prerequisite: MATH 2350H 60% or higher in MATH 2200H. Excludes MATH 3320H.

An introduction to the concepts, techniques, and applications of linear programming and discrete optimization. Topics include the simplex method, duality, game theory, and integer programming. Prerequisite: MATH 1350H.

Cross-listed: COIS-3350H

Linear and generalized linear models, introduction to smoothing and simulation, additive models, and topics in distributions and dimensionality. Prerequisite: MATH 2350H and 2560H.

An introduction to graph theory with emphasis on both theory and applications (algorithms). Topics may include graph terminology; trees; Eulerian and Hamiltonian properties of graphs; planarity; colourings; matchings. Prerequisite: MATH 2200H or MATH-COIS 2600H. Not open to students with credit for MATH 3600H or 4610H.

Complex numbers, limits and series. Complex functions, holomorphic functions. Complex contour integrals; Cauchy integral theorems. Taylor series. Laurent series. Calculus of residues. The Fundamental Theorem of Algebra. Frequency analysis: Fourier transforms, Laplace transforms, Fourier series, Z-transforms. Prerequisite: MATH 2120H.

A survey of the development of mathematics from pre-history to the modern era, with a focus on the development and spread of number systems and arithmetic techniques, proofs, algebra, and applications. Prerequisite: MATH 1120H. Recommended: MATH 2200H or 2350H. Not open to students with credit for MATH 3810H or 3820H.

Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course; or permission of department chair.

Classical mechanics of particles, rigid bodies, and continuous media. Topics include Lagrangian and Hamiltonian mechanics, systems of particles, motion of rigid bodies, and oscillating systems. Prerequisite: MATH 2110H 2150H , and PHYS-MATH 3130H. Excludes PHYS-MATH 3140H.

Cross-listed: PHYS-4140H

Covers classic topics in mathematical biology, including population biology, epidemiology, and mathematical ecology of a single or interacting species. The course addresses modeling of life-science problems by using difference/differential equations and applications of dynamical systems theories. Prerequisite: MATH-PHYS 3150H.

Cross-listed: BIOL-4230H

Provides the fundamental mathematical methods that are required to understand advanced topics in economics and to analyze economic models. Also useful for students who intend to pursue graduate studies in in economics, business, or applied mathematics. Topics include differential equations, difference equations, optimization, optimal control theory, and calculus of variation. Prerequisite: ECON 3250H or both MATH 2110H and MATH 2150H.

Cross-listed: ECON-4251H

Rings, subrings, quotient rings and ring homomorphisms. Ideal theory. Polynomial rings. Integral domains and fields of quotients. Fields, finite fields. Field extensions. Isomorphism Theorems for rings. The Fundamental Theorem of Galois Theory. Prerequisite: 60% or higher in MATH 3310H or permission of instructor. Excludes MATH 3360H.

Basic mathematical theory and computational techniques for how financial institutions can quantify and manage risks in portfolios of assets. Topics include: mean-variance portfolio analysis, the capital asset pricing model and Value at Risk (VaR). Prerequisite: MATH 2110H and MATH 2570H.

Introduction to stochastic processes, stationarity, and time series models: AR, MA, ARMA, and ARIMA. Prediction and extrapolation. Introduction to the Fourier transform and spectral theory for time series. Prerequisite: MATH 2560H and one of MATH 3560H or 2570H 3561H.

Working under the guidance of an approved faculty supervisor, students independently study an area of mathematics, write a paper on the topic, and give a presentation describing the research conducted. Prerequisite: Any two of MATH 3150H, 3160H, 3200H, 3310H, 3510H, 3560H, 3600H, 3770H, or 3790H.

Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course, or permission of department chair.

Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course, or permission of department chair.