Courses

Designed for students needing to strengthen their math background in preparation for further courses in mathematics or the sciences. Topics include rational numbers, decimal representation, real numbers, inequalities, algebraic expressions; trigonometry; functions, including algebraic, exponential, logarithmic, and trigonometric functions; analytic geometry; simple sequences and series. 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.

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.

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.

Linear regression models, goodness-of-fit 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.

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. Offered only at Trent University Durham.

Cross-listed: CCTH-1080H

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.

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.

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.

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.

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. 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. Logic, abstraction, proof techniques. Basic combinatorics. Sets, functions, (in/sur/bi)jections. Cantor's transfinite arithmetic. Number theory: divisibility, prime factorization, modular arithmetic. Prerequisite: MATH 1120H (or 1100Y or 1101Y) or 1350H.

Elements of Euclidean geometry, stressing links to modern mathematical methods. Geometric transformations and symmetry. Recommended for Education students. Prerequisite: One of MATH 1005H, 1110H, 1100Y, 1101Y, 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 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 (or 1100Y or 1101Y).

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 1350H, 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 1100Y or 1101Y); or COIS 1020H, MATH 1005H, and 1350H.

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

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

Error analysis, nonlinear equations, linear systems, interpolation methods, numerical differentiation and integration and initial value problems. Prerequisite: 60% or higher in MATH 1005H or 1110H. 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.

Public vs. private key cryptosystems: cyphertexts, plaintexts, and Kerkhoff's principle. Shannon's theory of perfect secrecy. Modular arithmetic: Chinese reminder theorem, Fermat/Euler theorems. RSA cryptosystem: definition and vulnerabilities. El-Gamal cryptosystem. Rabin cryptosystem. Quadratic residue theory. Probabilistic primality tests and factoring algorithms. Optional: discrete logarithm algorithms and elliptic curve cryptosystems. Prerequisite: MATH 2200H. Recommended: MATH-COIS 2600H or both MATH 1550H and COIS 2020H.

Cross-listed: COIS-3210H

Elements of projective and non-Euclidean geometry, including an introduction to axiomatic systems. Prerequisite: MATH 1110H (or 1100Y or 1101Y) or 1350H.

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

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 2200H and 2350H; or permission of instructor. MATH 3310H strongly recommended.

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.

Linear and generalized linear models, introduction to smoothing and simulation, additive models, and topics in distributions and dimensionality. Prerequisite: MATH 1350H and 2560H. Recommended: MATH 2350H.

Basics of three increasingly popular areas of discrete mathematics (discrete/computational geometry, combinatorial designs, error-correcting codes) and some connections between them. Topics may include Art Gallery problem, triangulations/flip graphs, affine/projective geometries; construction techniques for popular combinatorial designs; basics of coding theory, linear codes, bounds on codes, and techniques for combining codes. Prerequisite: MATH 2200H and MATHCOIS 2600H, or permission of instructor

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 transform, Laplace transform, Fourier series, Z-transform. Prerequisite: MATH 2120H.

The real number system. Limits. Continuity. Differentiability. Mean-value theorem. Convergence of sequences and series. Uniform convergence. Prerequisite: 60% or higher in MATH 1120H (or 1100Y or 1101Y) and 2200H.

Traces the historical development of mathematics from prehistory to medieval times, and the interactions between the development of mathematics and other major trends in human culture and civilization. We study the mathematics of ancient Egypt and Mesopotamia, and classical Greece and Rome. Prerequisite: MATH 1120H (or 1100Y or 1101Y). Recommended: MATH 2200H or 2350H.

Traces the development of mathematical ideas, abstraction, and proofs. The genesis of modern arithmetic in medieval India, the birth of algebra in the Islamic world, and their influence on medieval European mathematics. Renaissance mathematics (polynomial equations, analytic geometry). The Enlightenment (calculus, number theory). The apotheosis of rigour since the nineteenth century. Prerequisite: MATH 1120H (or 1100Y or 1101Y). Recommended: MATH 2200H or 2350H.

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 2150H.

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

Deals with a variety of numerical methods for solving ordinary and partial differential equations arising from scientific and engineering applications. Topics include finite difference, adaptive techniques, multi-step methods, Runge-Kutta methods, direct and iterative methods for systems, stability and convergence. Prerequisite: MATH 2150H and 3180H (or 2180H).

An introduction to the syntax and semantics of propositional and first-order logics through the Soundness, Completeness, and Compactness Theorems. Prerequisite: MATH 2200H.

Cross-listed: COIS-4215H

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 2150H.

Cross-listed: BIOL-4230H

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 1550H and 2110H.

Selected topics in statistics, including time series analysis, advanced modeling and regression, computational statistics, and computational algorithms for statistics. Prerequisite: MATH 2560H and one of MATH 3560H or 3570H. Recommended: MATH 2350H.

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 2350H and 2560H. Recommended: MATH 3560H.

Discrete- and continuous-time Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Poisson processes, queuing theory. Prerequisite: MATH 2570H and one of MATH 3700H, 3770H, or 3790H.

An introduction to graph theory with emphasis on both theory and applications and algorithms related to computer science, operation research, and management science. Prerequisite: MATH 2200H or MATH-COIS 2600H.

An introduction to combinatorics. The topics include counting techniques, generating functions, and block design. Prerequisite: MATH 2200H.

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, 3310H, 3350H, 3510H, 3560H, 3570H, 3610H, 3770H, or 3790H.

Students are placed in research projects with community organizations in the Peterborough area. Each placement is supervised jointly by a faculty member and a representative of a community organization. For details see Community-Based Research Program (p. 265). Prerequisite: MATH 2560H and either MATH 3560H or 4561H or 4562H and a cumulative average of at least 75%. Students may take either MATH 4850Y or, one or both of 4851H and 4852H for credit.

Students are placed in research projects with community organizations in the Peterborough area. Each placement is supervised jointly by a faculty member and a representative of a community organization. For details see Community-Based Research Program (p. 265). Prerequisite: MATH 2560H and either MATH 3560H or 4561H or 4562H and a cumulative average of at least 75%. Students may take either MATH 4850Y or, one or both of 4851H and 4852H for credit.