Courses
Course Listings Results Block
Please visit the Academic Timetable to see which courses are presently being offered and in which location(s). Not all courses listed below run every term or in all locations. For specific details about program requirements and degree regulations, please refer to the Academic Calendar.

MATH1001H: Precalculus Mathematics
Offered:
 Peterborough
Designed for students needing to strengthen their math background in preparation for further courses in mathematics or the sciences. Topics include rational numbers, real numbers, inequalities, algebraic expressions; trigonometry; functions, including algebraic, exponential, logarithmic, and trigonometric functions; equations; graph transformations; analytic geometry; and applications. Prerequisite: Ontario Grade 11 Functions and Relations (MCR3U) or equivalent. Not open to students enrolled in or with credit for any MATH courses other than MATH 1050Y, 1051H, 1052H, 1350H, or 2080Y. Does not satisfy the Mathematics requirement for a Bachelor of Science degree. Not for credit toward a major or minor in Mathematics.

MATH1005H: Applied Calculus
Offered:
 Peterborough
An introduction to the methods and applications of calculus. Derivatives, exponential and logarithmic functions, optimization problems, related rates, integration, partial derivatives, differential equations. Selected applications from the natural and social sciences. Prerequisite: A Grade 12U mathematics course or its equivalent. Not open to students enrolled in or with credit for MATH 1100Y, 1101Y, 1110H, or 1120H. Not for credit toward a major or minor in Mathematics.

MATH1051H: NonCalculus Statistics I: Elementary Probability and Statistics
Offered:
 Peterborough
 Durham GTA
Data summary, elementary probability, discrete and continuous distributions, the central limit theorem, estimation and hypotheses testing. This course uses high school mathematics as a foundation and involves the use of computer software. Not open to students enrolled in or with credit for MATH 2560H. Not for credit toward a major or minor in Mathematics. Excludes MATH 1050Y.

MATH1052H: NonCalculus Statistics II Elementary Statistical Methods
Offered:
 Peterborough
 Durham GTA
Linear regression models, goodnessoffit and analysis of contingency tables, analysis of variance for completely randomized design, randomized block design and factorial design, nonparametric tests. Use of computer methods for analysis of real data sets. Prerequisite: MATH 1051H. Not for credit toward a major or minor in Mathematics. Excludes MATH 1050Y.

MATH1080H: Math for Everyday Life
Offered:
 Peterborough
Should you buy a ticket for 6/49 or Super 7? If you test positive for a rare disease, what is the chance that you actually have it? How are E. coli bacteria and interest rates related? These are some of the questions we investigate in this course. We also look into the use, misuse, and abuse of mathematics in the media. Prerequisite: Ontario Grade 11 Functions & Relations (MCR3U) or equivalent. Not open to students enrolled in or with credit for any other MATH courses. Does not satisfy the Mathematics requirement for a Bachelor of Science degree. Not for credit toward a major or minor in Mathematics.

MATH1110H: Calculus I: Limits, Derivatives, and Integrals
Offered:
 Peterborough
 Durham GTA
Limits, differentiation, and integration through the basic substitution rule, with applications to other areas of mathematics and the physical and social sciences. Prerequisite: Grade 12 Advanced Functions or equivalent with at least 60%. Strongly recommended: Grade 12U Calculus and Vectors. Excludes MATH 1100Y, 1101Y.

MATH1120H: Calculus Ii: Integrals and Series Integrals
Offered:
 Peterborough
 Durham GTA
Techniques and applications of integration, sequences, series, and power series, with applications to other areas of mathematics and the physical and social sciences. Prerequisite: MATH 1110H. Excludes MATH 1100Y, 1101Y.

MATH1350H: Algebra I: Linear Algebra
Offered:
 Peterborough
 Durham GTA
Vectors, systems of linear equations, matrices, determinants, linear transformations, eigenvalues, and eigenvectors. Prerequisite: A Grade 12U mathematics course with at least 60%. Recommended: Grade 12U Calculus and Vectors.

MATH1550H: Introduction to Probability
Offered:
 Peterborough
 Durham GTA
Probability, random variables, probability distributions. Does not count as the Introductory Statistics course required for admission to some professional schools. Prerequisite: MATH 1005H or 1110H or 1100Y or 1101Y or permission of instructor.

MATH2081H: Math for Teacher Ed: Numbers & Geometry
Offered:
 Peterborough
 Durham GTA
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 MATHEDUC 2080Y.
Crosslisted: EDUC2081H

MATH2082H: Math for Teachers: Growth, Statistics
Offered:
 Peterborough
 Durham GTA
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 MATHEDUC 2080Y. Does not satisfy the Mathematics requirement for a Bachelor of Science degree.
Crosslisted: EDUC2082H

MATH2110H: Calculus Ill: Several Variables
Offered:
 Peterborough
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.

MATH2120H: Calculus Iv: Vector Calculus
Offered:
 Peterborough
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.

MATH2130H: Introductory Classical Dynamics
Offered:
 Peterborough
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 calculusbased methods and scientific computing tools to solve problems. Prerequisite: 60% or higher in PHYS 1001H and MATH 1120H. Pre or corequisite: MATH 2150H. Strongly recommended: COIS 1020H. Excludes PHYS 2110H, PHYSCOIS 2310H, PHYSMATH 3130H.
Crosslisted: PHYS2130H

MATH2150H: Ordinary Differential Equations
Offered:
 Peterborough
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.
Crosslisted: PHYS2150H

MATH2200H: Mathematical Reasoning
Offered:
 Peterborough
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.

MATH2260H: Euclidean Geometry
Offered:
 Peterborough
Elements of Euclidean geometry, stressing its axiomatic development. Recommended for Education students. Prerequisite: One of MATH 1005H, 1110H, or 1350H.

MATH2350H: Linear Algebra II Vector Spaces
Offered:
 Peterborough
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.

MATH2560H: Mathematical Statistics
Offered:
 Peterborough
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.

MATH2570H: Probability ll: Intermediate Probability
Offered:
 Peterborough
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.

MATH2600H: Discrete I: Structures
Offered:
 Peterborough
 Durham GTA
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.
Crosslisted: COIS2600H

MATH3130H: Classical Mechanics
Offered:
 Peterborough
Classical mechanics of particles in three dimensions. Topics include motion in noninertial reference frames, gravity, central forces, and special relativity. Prerequisite: PHYSMATH 2130H (or PHYS 2110H). Pre or corequisite: MATH 2110H and 2150H.
Crosslisted: PHYS3130H

MATH3150H: Partial Differential Equations
Offered:
 Peterborough
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.
Crosslisted: PHYS3150H

MATH3160H: Methods of Applied Mathematics
Offered:
 Peterborough
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: MATH 2110H and MATHPHYS 2150H. Recommended: MATH 2200H.
Crosslisted: PHYS3160H

MATH3180H: Numerical and Computational Methods
Offered:
 Peterborough
Error analysis, nonlinear equations, linear systems, interpolation methods, numerical differentiation and integration and initial value problems. Prerequisite: MATH2110H. Excludes MATHCOIS 2180H.
Crosslisted: COIS3180H

MATH3200H: Number Theory
Offered:
 Peterborough
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.

MATH3510H: Mathematical Finance
Offered:
 Peterborough
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, BlackScholes model. Historical and implied volatility. Prerequisite: MATH 1550H and 2150H.

MATH3561H: Statistics III: Advanced Statistics
Offered:
 Peterborough
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.

MATH3630H: Discrete II: Graph Theory
Offered:
 Peterborough
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 MATHCOIS 2600H. Not open to students with credit for MATH 4610H.

MATH3770H: Complex Analysis
Offered:
 Peterborough
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, Ztransforms. Prerequisite: MATH 2120H.

MATH3790H: Analysis I: Real Analysis
Offered:
 Peterborough
The real number system. Limits and continuity. Differentiability. Meanvalue theorem. Convergence of sequences and series. Uniform convergence. Completeness. Prerequisite: 60% or higher in MATH 2200H.

MATH3830H: Survey of the History of Mathematics
Offered:
 Peterborough
A survey of the development of mathematics from prehistory 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.

MATH4120H: Mathematical Modeling I
Offered:
 Peterborough
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: MATHPHYS 3150H.

MATH4140H: Advanced Classical Mechanics
Offered:
 Peterborough
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 PHYSMATH 3130H. Excludes PHYSMATH 3140H.
Crosslisted: PHYS4140H

MATH4230H: Mathematical Biology
Offered:
 Peterborough
Covers classic topics in mathematical biology, including population biology, epidemiology, and mathematical ecology of a single or interacting species. The course addresses modeling of lifescience problems by using difference/differential equations and applications of dynamical systems theories. Prerequisite: MATHPHYS 3150H.
Crosslisted: BIOL4230H

MATH4360H: Algebra Iv: Rings & Fields
Offered:
 Peterborough
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.

MATH4560H: Statistics IV: Topics in Statistics
Offered:
 Peterborough
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.

MATH4561H: Statistics V: Sampling and Experimental
Offered:
 Peterborough
Sampling and design of experiments. Topics in design of experiments include ANOVA, randomized block designs, factorial designs, blocking and confounding in factorial designs, response surface methods. Topics in sampling include simple random, systematic, stratified and cluster sampling, sample size estimation, unequal probability sampling, and multistage designs. Prerequisite: MATH 3560H.

MATH4570H: Probability III: Stochastic Processes
Offered:
 Peterborough
Discrete and continuoustime Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Poisson processes, queuing theory. Prerequisite: MATH 2200H and 2570H.

MATH4630H: Discrete III: Combinatorics
Offered:
 Peterborough
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: MATHCOIS 2600H or MATH 3630H. Not open to students with credit for MATH 4620H.

MATH4790H: Analysis II: Topology and Measure
Offered:
 Peterborough
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.

MATH4800H: Mathematics Honours Project
Offered:
 Peterborough
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.

MATH4903H: Reading/Seminar Course
Offered:
 Peterborough
Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course, or permission of department chair.