Courses
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.
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| Course Code | Description | Cross Listed With |
|---|---|---|
| MATH-1001H | Precalculus Mathematics 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. | |
| MATH-1005H | Applied Calculus 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. | |
| MATH-1051H | Non-Calculus Statistics I: Elementary Probability and Statistics 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. | |
| MATH-1052H | Non-Calculus Statistics II Elementary Statistical Methods 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. | |
| MATH-1080H | Math for Everyday Life 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. | CCTH-1080H |
| MATH-1110H | Calculus I: Limits, Derivatives, and Integrals 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. | |
| MATH-1120H | Calculus Ii: Integrals and Series Integrals 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. | |
| MATH-1350H | Linear Algebra I Matrix Algebra 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. | |
| MATH-1550H | Introduction to Probability 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. |
| Course Code | Description | Cross Listed With |
|---|---|---|
| MATH-2080Y | Math for Teacher Education A course in mathematics and mathematical thinking for prospective elementary school teachers. Number systems and counting, graphs and networks, symmetry and patterns, mathematics in nature and art, probability and statistics, measurement and growth. 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. | |
| MATH-2110H | Calculus Ill: Several Variables 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. | |
| MATH-2120H | Calculus Iv: Vector Calculus 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. | |
| MATH-2150H | Ordinary Differential Equations 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. | PHYS-2150H |
| MATH-2200H | Mathematical Reasoning 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. | |
| MATH-2260H | Geometry I Euclidean Geometry 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. | |
| MATH-2350H | Linear Algebra II Vector Spaces 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. | |
| MATH-2560H | Applied Statistics I 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). | |
| MATH-2570H | Probability II: Stochastic Processes Covers a variety of important models used in modelling of random events that evolve in time. These include Markov chains (both discrete and continuous), Poisson processes and queues. The rich diversity of applications of the subject is illustrated through varied examples. Prerequisite: MATH 1550H and 1350H. Excludes MATH 3570H. | |
| MATH-2600H | Discrete Structures 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. | COIS-2600H |
| Course Code | Description | Cross Listed With |
|---|---|---|
| MATH-3130H | Classical Mechanics Particle motion in one dimension, resistive forces. Oscillatory motion, waves on a string, acoustic waves in gases, harmonic oscillator, damped, and damped, driven oscillators, resonance, Q-factor. Fourier Series. Particle motion in three dimensions, conservative forces and fields. Accelerated coordinate systems and inertial forces. Central forces, gravitation, Kepler's Laws, spacecraft motion, stability of orbits. Prerequisite: 60% or higher in PHYS 1002H (or 1000Y) and in MATH 1120H (or 1100Y or 1101Y), or permission of the department. Pre- or co-requisite: MATH 2110H and 2150H. | PHYS-3130H |
| MATH-3150H | Partial Differential Equations The heat equation, wave equation, telegraph equation, Laplace equation, Poisson equation and Schrodinger equation, in one, two, and three dimensions, in Cartesian, Polar, and/or Spherical coordinates. Physical interpretations. Properties of harmonic functions. Classification of PDEs. 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. | PHYS-3150H |
| MATH-3160H | Methods of Applied Mathematics 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. | PHYS-3160H |
| MATH-3180H | Intro to Numerical and Computation Meth 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. | COIS-3180H |
| MATH-3200H | Number Theory 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. | |
| MATH-3210H | Mathematical Cryptography 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. | COIS-3210H |
| MATH-3260H | Geometry II Projective Non Euclidean Elements of projective and non-Euclidean geometry, including an introduction to axiomatic systems. Prerequisite: MATH 1110H (or 1100Y or 1101Y) or 1350H. | |
| MATH-3310H | Algebra III Abstract Algebra 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, 3360H. | |
| MATH-3350H | Linear Programming 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. | COIS-3350H |
| MATH-3510H | Mathematical Finance 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. | |
| MATH-3560H | Linear Statistical Models 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. | |
| MATH-3610H | Discrete Optimization An introduction to the concepts, techniques, and applications of discrete optimization. Topics include integer programming, dynamic programming, network optimization, and approximation methods for NP hard problems. Prerequisite: MATH 1350H and one of MATH 2200H or MATH-COIS 2600H. | |
| MATH-3700H | Metric Geometry & Topology Metric spaces. Limits and continuity. Completeness: the Baire Category Theorem; normed linear spaces and Banach spaces; the Contraction Mapping Theorem and applications. Compact, separable, and (first/ second) countable spaces: the Heine-Borel and Lindelof theorems. Topological spaces. Hausdorff axiom and (non) metrizability. Product spaces and quotient spaces. Compactness and Tychonoff's theorem. (Path)- connectedness. Prerequisite: MATH 1120H (or 1100Y or 1101Y) and 2200H. | |
| MATH-3770H | Analysis II Complex Analysis 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. | |
| MATH-3790H | Real Analysis 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. | |
| MATH-3810H | Ancient & Classical Mathematics 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. | |
| MATH-3820H | Mathematics From Medieval to Modern Time 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. | |
| MATH-3900Y | Reading/Seminar Course Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course; or permission of department chair. | |
| MATH-3901H | Reading Course Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course; or permission of department chair. | |
| MATH-3902H | Reading Course Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course; or permission of department chair. |
| Course Code | Description | Cross Listed With |
|---|---|---|
| MATH-4140H | Advanced Classical Mechanics Applied mathematics as found in the classical mechanics of particles, rigid bodies, and continuous media. Motion of rigid bodies, Lagrangian mechanics, Hamiltonian mechanics, dynamics of oscillating systems. Prerequisite: MATH 2110H 2150H , and PHYS-MATH 3130H. Excludes PHYS-MATH 3140H. | PHYS-4140H |
| MATH-4180H | Advanced Numerical Methods 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). | |
| MATH-4510H | Mathematical Risk Management 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. | |
| MATH-4561H | Sampling and Design of Experiments 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. | |
| MATH-4610H | Introduction to Graph Theory 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. | |
| MATH-4620H | Combinatorics An introduction to combinatorics. The topics include counting techniques, generating functions, and block design. Prerequisite: MATH 2200H. | |
| MATH-4710H | Chaos Symbolic Dynamics Fractals An introduction to discrete dynamical systems. Periodicity, attraction. Parametrized families of functions, bifurcation, chaos. Symbolic dynamics, conjugacy, Cantor Sets. Deterministic fractals, fractal dimension, Lyapunov exponents, entropy. Prerequisite: MATH 3700H, 3770H, or 3790H. | |
| MATH-4800H | Mathematics Honours Project 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. | |
| MATH-4810H | Perspectives in Mathematics I Team-taught by three instructors. Each instructor teaches a four-week module on a special topic. Prerequisite: 60% or higher in 1.0 3000- or 4000-level MATH credit. | |
| MATH-4900Y | Reading/Seminar Course Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course, or permission of department chair. | |
| MATH-4903H | Reading/Seminar Course Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course, or permission of department chair. | |
| MATH-4904H | Reading/Seminar Course Details may be obtained by consulting the department. Prerequisite: 85% minimum in any prerequisite for the course, or permission of department chair. |