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Math & Stats Courses

MATH 1000 MATH 1300 MATH 2200 MATH 3170 STAT 1200
MATH 1070 MATH 1380 MATH 2240 MATH 3200 STAT 2000
MATH 1100 MATH 1390 MATH 2700 MATH 3220 STAT 3050
MATH 1130 MATH 1420 MATH 3000 MATH 3400 STAT 3060
MATH 1140 MATH 1540 MATH 3020 MATH 3510 STAT 4040
MATH 1150 MATH 1640 MATH 3030 MATH 3650 STAT 4990
MATH 1170 MATH 1700 MATH 3070 MATH 3700
MATH 1230 MATH 1900 MATH 3080 MATH 4410
MATH 1240 MATH 2110 MATH 3120 MATH 4430
MATH 1250 MATH 2120 MATH 3160
MATH 1000

MATH 1000

Pre-Calculus (5,0,0) 3 credits

This course is designed to prepare students for calculus. Topics include functional notation, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, and an introduction to the derivative.

Prerequisite: Principles of Math 12, or MATH 0610, or B or better in MATH 0600

MATH 1070

MATH 1070

Fundamentals of Mathematics for Business and Economics (3,1,0) 3 credits

This course is designed for Business and Economics students. Topics include the review of linear and non-linear functions and models (including cost, revenue, profit, demand and supply), solving linear and non-linear systems of equations, matrices, linear programming, difference equations and mathematics of finance (including simple and compound interest: discrete and continuous, annuities, mortgages, loans).

Prerequisite: Principles of Math 12 or MATH 1000 or MATH 0600 (any of them within the last two years). In exceptional cases, for example, where a student has transferred from another educational system or has been out of school for several years, entry to MATH 1070 may be permitted based on placement test administered (for this exceptional case only) by the Department of Mathematics and Statistics during the first week of classes.

MATH 1100

MATH 1100

Finite Mathematics with Applications 1 (3,1,0) 3 credits

Intended primarily for Liberal Arts or Education students, MATH 1100 is not acceptable for credit in Science. The past twenty years have seen an explosive growth in the scope of mathematics so much that many of the Social Sciences are employing mathematics as a powerful research tool. This course is designed to expose students to the areas of mathematics that they are likely to require in future studies. Topics to be covered include: counting, probability, matrices, linear programming, and Markov chains or difference equations.

Prerequisite: C standing in Principles of Math 11, Applications of Math 12 or MATH 0510, or equivalent

MATH 1130

MATH 1130

Enriched Calculus 1 (3,1,0) 3 credits

This course covers single-variable differential calculus and its applications in more depth than MATH 1140, to provide a strong foundation for further study in mathematical disciplines. It is a required course for students in the Engineering Transfer program.

Prerequisite: A in Principles of Math 12, or admission to the Engineering program

Note: Students who already have credit for MATH 1140, MATH 1150 or MATH 1170 may not take MATH 1130 for further credit

MATH 1140

MATH 1140

Calculus 1 (3,1,0) or (5,0,0) 3 credits

This course covers differential calculus for functions of one variable, with applications emphasizing the physical sciences. Topics include calculation and interpretation of limits and derivatives, curve sketching, optimization and related-rate problems, and Newton’s method. The Computer Algebra System “Maple” is introduced as a tool for calculus.

Prerequisite: At least C+ in Principles of Math 12 or MATH 1000 within the last two years or at least C+ in MATH 0610 within the last two years. In exceptional cases, for example, where a student has transferred from another educational system or has been out of school for several years, entry into MATH 1140 may be permitted based on a placement test administered (for these exceptional cases only) by the Department of Mathematics and Statistics during the first week of classes.

Note: Students who have never studied calculus before, or who barely satisfy the course prerequisites, are advised to register in a section vectored (5,0,0). Students who already have credit for MATH 1130, MATH 1150 or MATH 1170 may not take MATH 1140 for further credit.

MATH 1150

MATH 1150

Calculus for the Biological Sciences 1 (3,1,0) or (5,0,0) 3 credits

This course covers differential calculus for functions of one variable, with applications emphasizing the biological sciences. Topics include calculation and interpretation of limits and derivatives, curve sketching, optimization problems, and Newton’s method.

Prerequisite: At least C+ in Principles of Math 12 or MATH 1000 within the last two years or at least C+ in MATH 0610 within the last two years. In exceptional cases, for example, where a student has transferred from another educational system or has been out of school for several years, entry into MATH 1150 may be permitted based on a placement test administered (for these exceptional cases only) by the Department of Mathematics and Statistics during the first week of classes.

Note: Students who already have credit for MATH 1130, MATH 1140, or MATH 1170 may not take MATH 1150 for further credit. Students planning to take second year Mathematics courses are encouraged to enroll in MATH 1140 and MATH 1240 or MATH 1130 and MATH 1230.

MATH 1170

MATH 1170

Calculus for Business and Economics (3,1,0) 3 credits

This course is intended for Business and Economic students. Topics include calculation and interpretation of derivatives, curve sketching, optimization (applied to business and economics), multivariable functions (including partial derivatives, optimization and Lagrange multipliers) and antiderivatives).

Prerequisite: At least C- in MATH 1070 or at least C+ in Principles of Math 12 or MATH 1000 or MATH 0610 (any of them within the last two years). In exceptional cases, for example, where a student has transferred from another educational system or has been out of school for several years, entry to MATH 1170 may be permitted based on placement test administered (for this exceptional case only) by the Department of Mathematics and Statistics during the first week of classes.

Note: Students who already have credit for MATH 1130, MATH 1140, or MATH 1150 may not take MATH 1170 for further credit

MATH 1230

MATH 1230

Enriched Calculus 2 (3,1,0) 3 credits

This course covers single-variable integral calculus and its applications in more depth than MATH 1240, to provide a strong foundation for further study in mathematical disciplines. It is a required course for students in the Engineering Transfer program.

Prerequisite: MATH 1130

MATH 1240

MATH 1240

Calculus 2 (3,1,0) or (5,0,0) 3 credits

This course covers integral calculus for functions of one variable, with applications emphasizing the physical sciences. Topics include Riemann sums, definite and indefinite integrals, techniques of integration, improper integrals, applications to area, volume, arc length, probability, physics, separable differential equations, and series.

Prerequisite: MATH 1140, or MATH 1130, or MATH 1150

Note: Students who already have credit for MATH 1250 may not take MATH 1240 for further credit. Students planning to take second year Mathematics courses are encouraged to enroll in MATH 1140 and MATH 1240 or MATH 1130 and MATH 1230.

MATH 1250

MATH 1250

Calculus for the Biological Sciences 2 (3,1,0) or (5,0,0) 3 credits

This course covers integral calculus for functions of one variable, with applications emphasizing the biological sciences. Topics include Riemann sums, definite and indefinite integrals, techniques of integration, improper integrals, first-order differential equations and slope fields, (applications to area, probability, logistic growth and predator-prey systems), and series.

Prerequisite: MATH 1130, or MATH 1140, or MATH 1150

Note: Students who already have credit for MATH 1240 may not take MATH 1250 for further credit. Students planning to take second year Mathematics courses are encouraged to enroll in MATH 1140 and MATH 1240 or MATH 1130 and MATH 1230.

MATH 1300

MATH 1300

Linear Algebra for Engineers (3,1,0) 3 credits

This course is designed for students in the first year Engineering Transfer program and covers vectors in R2 and R3, linear transformations, matrices and elimination, eigenvalues and eigenvectors and their application to Engineering problems. A computer lab component will be used to explore applications.

Prerequisite: Admission to the Engineering program.

Corequisite: MATH 1130 or MATH 1140

MATH 1380

MATH 1380

Discrete Structures 1 for Computing Science (3,1,0) 3 credits

An introduction to the basic mathematical concepts used in computing science. Topics covered include the binary number system, computer arithmetic, logic and truth tables, Boolean algebra, logic gates and simple computer circuits, sets, relations, functions, vectors and matrices, counting, probability theory and statistics (mean, variance, median, mode, random variables).

Prerequisite: A grade of C+ or better in any of Principles of Math 12, Applications of Math 12, or MATH 0610; or B or better in MATH 0600, or C+ or better in Physics 12, or instructors written consent

Note: Same as COMP 1380. Students who already have credit for MATH 1700 may not take MATH 1380 for further credit.

MATH 1390

MATH 1390

Discrete Structures 2 for Computing Science (3,1,0) 3 credits

A continuation of MATH 1380, this course introduces further mathematical concepts used in computing science. Topics covered include graph theory in terms of directed graphs, binary trees, languages, grammars, machines, an introduction to proofs and mathematical induction, and algorithm analysis.

Prerequisite: C or better in COMP 1380 or MATH 1380; or MATH 1070, or instructor’s written consent

Note: Same as COMP 1390. Students who already have credit for MATH 1700 may not take MATH 1390 for further credit.

MATH 1420

MATH 1420

Mathematics for Visual Arts (3,1,0) 3 credits

This course will study mathematical concepts and techniques useful in a visual arts context. Topics will include real numbers, ratios, geometry, and perspective.

Prerequisite: Principles of Math 11 or Applications of Math 11 or equivalent

MATH 1540

MATH 1540

Technical Mathematics 1 (3,1,0) 3 credits

Topics covered will include trigonometry, introduction to two- and three- dimensional vectors, functions and graphs, solving linear and quadratic equations, systems of linear equations, matrices, coordinate geometry, areas and volumes of standard geometric shapes, and problem solving.

Prerequisite: Admission to the Architectural and Engineering Technology program

MATH 1640

MATH 1640

Technical Mathematics 2 (3,1,0) 3 credits

This is a course in calculus for students in the Engineering Design and Drafting Technology program. The course covers both differentiation and integration, with applications to curve sketching, extreme values and optimization, related rates, areas, volumes and lengths of curves.

Prerequisite: Admission to the Architectural and Engineering Technology program

MATH 1700

MATH 1700

Discrete Mathematics 1 (3,1,0) 3 credits

This course is an introduction to the foundation of modern mathematics including basic set theory; counting; solutions to recurrence relations; logic and quantifiers; properties of integers; mathematical induction; asymptotic notation; introduction of graphs and trees; finite state machines and formal languages; Boolean algebra.

Prerequisite: A minimum grade of C+ in Principles of Math 12 or MATH 1000 or a minimum grade of C+ in MATH 0610 within the last two years or permission of the instructor

Note: Students who already have credit for MATH 1380 and MATH 1390 may not take MATH 1700 for further credit

MATH 1900

MATH 1900

Principles of Mathematics for Teachers (3,1,0) 3 credits

This course is primarily for students who wish to enter the Elementary Teaching program. Basic mathematical concepts are examined, with some exposure to teaching techniques applicable in the classroom. Topics include measurement, problem solving, number systems, probability, statistics counting theory, functions numeration, exponents, ratios, and interest.

Prerequisite: None

MATH 2110

MATH 2110

Calculus 3 (3,1,0) 3 credits

The concepts of single-variable calculus are extended to higher dimensions by using vectors or variables. Topics include the following: vector geometry and the analytic geometry of lines, planes and surfaces; calculus of curves in two or three dimensions, including arc length and curvature; calculus of scalar-valued functions of several variables, including the gradient, directional derivatives and the Chain Rule; Lagrange multipliers and optimization problems; double integrals in rectangular and polar coordinates.

Prerequisite: MATH 1230 or 1240 or equivalent; MATH 1300 for EECE Year 2 students

Corequisite: MATH 2120 recommended if MATH 1300 not previously completed

MATH 2120

MATH 2120

Linear Algebra 1 (3,1,0) 3 credits

This is an introductory course in linear algebra, covering vector spaces, bases and dimension, geometry of n-dimensional space, linear transformations and systems of linear equations.

Prerequisite: MATH 1240 or equivalent calculus

MATH 2200

MATH 2200

Introduction to Analysis (3,1,0) 3 credits

Analysis is a broad area of mathematics that includes calculus. This course presents some basic concepts of analysis in a mathematically rigorous manner, using theorems and proofs. Students are expected to develop some ability to understand proofs and to write their own proofs. After a survey of essential background material on logic, set theory, numbers and functions, the course covers suprema and infima of sets, completeness, basic metric topology of the real numbers (neighbourhoods, interior points and cluster points), continuity and limits.

Prerequisite: MATH 1240 or equivalent calculus. B- minimum strongly recommended.

MATH 2240

MATH 2240

Differential Equations 1 (3,1,0) 3 credits

This course deals with ordinary differential equations and related initial-value problems, emphasizing their many applications in science and engineering. Methods are discussed for solving such equations either exactly or approximately. Topics include first-order equations, higher order linear equations, modelling with differential equations, systems of linear equations, and phase plane analysis of nonlinear systems.

Prerequisite: MATH 2110 and MATH 2120

MATH 2700

MATH 2700

Discrete Mathematics 2 (3,1,0) 3 credits

This course is a continuation of discrete mathematics from MATH 1700, covering combinatorial arguments and proofs; deriving recurrence relations; generating functions; inclusion-exclusion; functions and relations; countable and uncountable sets; graphs.

Prerequisite: MATH 1700 with a minimum grade of C-

Mathematics upper level course note

Note: Most 3rd and 4th year math courses are offered in alternate years.

MATH 3000

MATH 3000

Complex Variables (3,1,0) 3 credits

This course introduces classical complex function theory, a cornerstone of mathematics. Topics include complex derivatives and the Cauchy-Riemann equations, the complex exponential function and related elementary functions, integration along curves and Cauchy’s theorems, Taylor and Laurent series, zeros and singularities, residues, and evaluation of integrals using the residue theorem.

Prerequisite: MATH 2200 or MATH 3170 (both are recommended) or admission to EECE Year 2 program

Corequisite: MATH 3170 for EECE Year 2 students

MATH 3020

MATH 3020

Introduction to Probability (3,1,0) 3 credits

This course provides a theoretical foundation for the study of statistics. Topics include basic notions of probability, random variables, probability distributions (both single-variable and multi-variable), expectation and conditional expectation, limit theorems and random number generation.

Prerequisite: MATH 2110

MATH 3030

MATH 3030

Introduction to Stochastic Processes (3,1,0) 3 credits

Simple random processes are studied, including discrete and continuous Markov chains, Poisson processes and Brownian motion. Renewal theory is also discussed.

Prerequisite: MATH 3020

MATH 3070

MATH 3070

Linear Algebra 2 (3,1,0) 3 credits

This is a continuation of MATH 2120. Topics include matrix diagonalization and its application to systems of linear differential equations and Markov chains, invariant subspaces, inner product spaces, Gram-Schmidt orthogonalization, linear operators of various special types (normal, self-adjoint, unitary, orthogonal, projections), the finite-dimensional spectral theorem, bilinear and quadratic forms.

Prerequisite: MATH 2120

MATH 3080

MATH 3080

Euclidean Geometry (3,1,0) 3 credits

The course begins with the axiomatic development of geometry, briefly exploring possible variations in axioms. This leads to a study of classical Euclidean geometry. Geometric transformations are introduced, with some discussion of their relevance to computer graphics. The course concludes with a look at some non-Euclidean geometries and projective geometry.

Prerequisite: MATH 2120

MATH 3120

MATH 3120

Introduction to Number Theory (3,1,0) 3 credits

The course begins with integer divisibility and the related ideas of prime numbers, unique prime factorization, and congruence. Attention is then directed to arithmetic functions, including the Euler totient function. The Chinese Remainder Theorem and quadratic reciprocity are studied, and some Diophantine equations are considered. Lastly, continued fractions and primitive roots are discussed.

Prerequisite: MATH 2120

MATH 3160

MATH 3160

Differential Equations 2 (3,1,0) 3 credits

This course has three parts. The first part examines some methods for solving ordinary differential equations. Power series methods are applied to obtain solutions near ordinary points and regular singular points, and the real Laplace transform is discussed. The second part deals with Sturm-Liouville boundary-value problems, Fourier series, and other series of eigenfunctions, including Fourier-Bessel series. The final part is an introduction to boundary-value problems involving partial differential equations, primarily the heat equation, the wave equation and Laplace’s equation, with applications in physics. The method of separation of variables is used.

Prerequisite: MATH 2240

Note: This course is the same as PHYS 3120

MATH 3170

MATH 3170

Calculus 4 (3,1,0) 3 credits

This course is a continuation of MATH 2110. Topics include triple integrals in rectangular, cylindrical and spherical coordinates, general change of variables in double and triple integrals, vector fields, line integrals, conservative fields, and path independence, Green’s theorem, surface integrals, Stokes’ theorem and the divergence theorem, with applications in physics.

Prerequisite: MATH 2110 or equivalent

MATH 3200

MATH 3200

Real Variables (3,1,0) 3 credits

This course is a continuation of MATH 2200. Most or all of the following topics are discussed: theorems of single-variable differential calculus, including the mean-value theorem, Taylor’s theorem and the inverse function theorem, Euclidean space and metric spaces, basic topology of metric spaces (neighbourhoods, open sets, connected sets), convergence in metric spaces, compactness, including the Bolzano-Weierstrass and Heine-Borel theorems, and integration.

Prerequisite: MATH 2200 (B- minimum strongly recommended) and at least one of MATH 3070, MATH 3080, MATH 3120 and MATH 3220

MATH 3220

MATH 3220

Abstract Algebra (3,1,0) 3 credits

This course introduces the abstract algebraic concepts of rings, fields, integral domains, homomorphisms and isomorphisms, concluding with a brief treatment of groups.

Prerequisite: MATH 2120 and at least one of MATH 2200, MATH 3070, MATH 3080 and MATH 3120

MATH 3400

MATH 3400

Introduction to Linear Programming (3,1,0) 3 credits

Algorithms for linear programming are introduced and studied for both theoretical and applied perspectives. Topics include the graphic method, simplex method, revised simplex method, and duality theory, as well as some special linear programming such as network flows and game theory.

Prerequisite: MATH 2120

MATH 3510

MATH 3510

Problem Solving in Applied Mathematics (3,1,0) 3 credits

This course will provide learners with a systematic approach to problem solving. The student will use a variety of analytical techniques to solve problems drawn from various disciplines. The course is of interest to students in any program where numerical problems may occur.

Prerequisite: C or better in any 1000 level Mathematics or Statistics course with the exceptions of MATH 1000 and MATH 1900

MATH 3650

MATH 3650

Numerical Analysis (3,1,0) 3 credits

This course introduces standard numerical methods, including algorithms for solving algebraic equations (linear and nonlinear, single equations and systems) and for polynomial approximation and interpolation.

Prerequisite: MATH 2110, MATH 2120

Note: Students who already have credit for COMP 3320 may not take MATH 3650 for further credit

MATH 3700

MATH 3700

Introduction to the History of Mathematics (3,1,0) 3 credits

The course will trace the development of numeration, arithmetic, geometry, algebra and other areas of mathematics from their beginnings to their modern forms. The historical development studies will be enhanced by the solution of mathematical problems using the techniques available in the period under study.

Prerequisite: MATH 1240 or equivalent

MATH 4410

MATH 4410

Modelling of Discrete Optimization Problems (3,1,0) 3 credits

Real-world optimization problems are formulated so that they can be tackled by standard techniques involving linear programming, network flows, dynamic programming and difference equations. Additional techniques may include post-optimality analysis, game theory, Markov chains, and matchings.

Prerequisite: MATH 3400

MATH 4430

MATH 4430

Introduction to Graph Theory (4,0,0) 3 credits

This introductory course deals mostly with non-algorithmic topics of graphs, including connectivity, Eulerian graphs, Hamiltonian graphs, planarity and Kuratowski’s theorem, matchings, graph colouring, and extremal graphs. Applications of graphs are discussed.

Prerequisite: MATH 2220 or at least 12 credits of Mathematics courses numbered 2000 or above (which can be taken concurrently)

STAT 1200

STAT 1200

Introduction to Statistics (3,1,0) 3 credits

This course is for non-science students who require an introduction to statistical reasoning. Topics include descriptive statistics, correlation and regression, normal and binomial distributions, sample and experimental design, chi-square distribution, and hypothesis testing.

Prerequisite: Principles of Math 11, or Applications of Math 12, or MATH 0510 or equivalent. MATH 1100 is recommended.

Note: Students may normally receive credit for only one of the following: BIOL 3000, BUEC 2320, MATH 1200, PSYC 2100, SOCI 2710, SOCI 3710, STAT 1200, STAT 2000


Mathematics Major Requirements

Honours Mathematics Requirements

BSc Prerequisite Checksheet

BSc Non Science Electives 2012



STAT 2000

STAT 2000

Introduction to Statistics (3,1,0) 3 credits

This course is for science and forestry students who require an introduction to probability and statistical reasoning. Topics include descriptive statistics, correlation and regression, probability, probability distributions, binomial and normal distributions, sample and experimental design, chi-square distribution, hypothesis testing, and analysis of variance. Applications in science and forestry are emphasized.

Prerequisite: MATH 1140 or equivalent first semester of calculus

Note: Students may normally receive credit for only one of the following: BIOL 3000, BUEC 2320, MATH 1200, PSYC 2100, SOCI 2710, SOCI 3710, STAT 1200, STAT 2000

STAT 3050

STAT 3050

Introduction to Statistical Inference (3,1,0) 3 credits

This course examines some of the theory behind statistical inference. Topics include a review of probability theory, sampling distributions, and methods of estimation and hypothesis testing, including maximum likelihood estimation, bootstrapping, Bayesian methods, likelihood ratio testing and confidence interval construction.

Prerequisite: STAT 2000 and MATH 3020

STAT 3060

STAT 3060

Applied Regression Analysis (3,1,0) 3 credits

This course concentrates on the applications rather than the theory of regression analysis. Topics include residual analysis, diagnostics, transformations, model selection and checking, weighted least squares and nonlinear models. Additional topics which may be included are inverse, robust, ridge and logistic regression.

Prerequisite: MATH 2120, STAT 2000

STAT 4040

STAT 4040

Analysis of Variance (3,1,0) 3 credits

This course discusses the analysis of variance for standard experimental designs. Topics include single factor designs, fixed and random effects, block designs, hierarchical designs, multiple comparisons, factorial designs, mixed models, general rules for analysis of balanced designs, and analysis of covariance.

Corequisite: STAT 3060

STAT 4990

STAT 4990

Selected Topics in Statistics (3,1,0) 3 credits

This course will consider in depth a selection of topics drawn from Statistics. The particular topics may vary each time the course is offered.

Prerequisite: At least two of MATH 3020, MATH 3030, STAT 3050, STAT 3060 or permission of the instructor