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 propositional logic, sets and relations, proofs, counting techniques and recursive relations, trees and networks (graphs); applications. 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 2110H and 2150H. Strongly recommended: MATH 1350H.

Cross-listed: PHYS-3150H

Error analysis, nonlinear equations, linear systems, interpolation methods, numerical differentiation and integration and initial value problems. Prerequisite: MATH-2110H. Excludes MATH-COIS 2180H.

Cross-listed: COIS-3180H

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

Elements of stochastic calculus. Discrete time market models and continuous time market models. Selffinancing strategies and arbitrage. Replication of claims. Completeness of market models. Pricing of derivatives: binomial model, Black-Scholes model. Historical and implied volatility. Prerequisite: MATH 1550H and 2150H.

Advanced statistical methods, especially in computational statistics: linear and generalized linear models; classification methods; variable selection; resampling; decision trees; neural networks; Markov Chain Monte Carlo methods; Bayesian estimation; multilevel and hierarchical models; and experimental design. Additional topics as time allows. Prerequisite: MATH 2560H or a minimum 75% in each of MATH 1051H and 1052H, or permission of instructor.

The real number system. Limits and continuity. Differentiability. Mean-value theorem. Convergence of sequences and series. Uniform convergence. Completeness. Prerequisite: 60% or higher in MATH 2200H.

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.

Provides an introduction to the mathematical modelling process and applies this process to simple mathematical modelling problems arising from a variety of application areas in science and engineering. Mathematical modelling techniques, such as differential equations, discrete systems, and numerical methods along with computer aids are utilized. Prerequisite: MATH-PHYS 3150H.

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

A senior topics course in Statistics. Topics may include time series analysis, clustering and classification, generalized linear models, computational statistics or similar. Prerequisite: MATH 2560H and one of MATH 3560H or 3561H.

Discrete- and continuous-time Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Poisson processes, queuing theory. Prerequisite: MATH 2200H and 2570H.

An introduction to combinatorics. Topics may include advanced counting techniques; Stirling numbers, Bell numbers and Catalan numbers; generating functions; Latin squares, block designs and Hadamard matrices. Prerequisite: MATH-COIS 2600H or MATH 3630H. Not open to students with credit for MATH 4620H.

Normed and metric spaces, open sets, continuous mappings, sequence and function spaces, completeness. Lebesgue measure on the line, the Lebesgue integral, monotone and dominated convergence theorems. Prerequisite: MATH 3790H. Not open to students with credit for MATH 3700H.

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.

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