At most 9 credit hours in Mathematics will be given for courses completed from the following list subject to normal credit restrictions: Mathematics 1000, 1031, 1050, 1051, 1080, 1081, 1090, 1150, 1151.

Mathematics courses are designated by MATH and Statistics courses are designated by STAT.

102F, 103F and 104F

Mathematics Skills Program

are non-credit courses intended for those students who either have a weak background in mathematics or are returning to the subject after some years. The program enables students to master mathematical operations such as those involving whole numbers, fractions, decimals, percents, integers, exponents, linear equations, algebraic and rational expressions, formulas, graphs, systems of linear equations, basic trigonometry, exponents and radicals, and quadratics.

1000

Calculus I

is an introduction to differential calculus, including algebraic, trigonometric, exponential, logarithmic, inverse trigonometric and hyperbolic functions. Applications include kinematics, related rates problems, curve sketching and optimization.

CR: the former MATH 1081

LH: 1.5

PR: MATH 1090 or a combination of placement test and high school Mathematics scores acceptable to the Department

1001

Calculus II

is an introduction to integral calculus, including Riemann sums, techniques of integration and improper integrals. Applications include exponential growth and decay, area between curves and volumes of solids of revolution.

CR: the former Engineering 1411, the former Engineering 2413

PR: MATH 1000 or the former MATH 1081

1050

Finite Mathematics I

covers topics which include sets, logic, permutations, combinations, and elementary probability.

CR: the former MATH 1150. With the exception of those already admitted at the time of registration in this course to a Bachelor of Education program that requires this course, students who already have obtained credit for 6 or more Mathematics credit hours numbered 2000 or above are not permitted to register for this course nor can they receive credit for it

LC: 4

PR: a combination of placement test and high school mathematics scores acceptable to the Department, or MATH 103F

1051

Finite Mathematics II

covers topics which include elementary matrices, linear programming, elementary number theory, mathematical systems and geometry.

CR: the former MATH 1151. With the exception of those already admitted at the time of registration in this course to a Bachelor of Education program that requires this course, students who already have obtained credit for 6 or more Mathematics credit hours numbered 2000 or above are not permitted to register for this course nor can they receive credit for it.

LH: 1.5

PR: a combination of placement test and high school mathematics scores acceptable to the Department, or MATH 103F

1090

Algebra and Trigonometry

provides students with the essential prerequisite elements for the study of an introductory course in calculus. Topics include algebra, functions and their graphs, exponential and logarithmic functions, trigonometry, polynomials, and rational functions.

CR: MATH 1000, MATH 1001, MATH 1080, or MATH 1081

LH: 3

PR: a combination of placement test and high school Mathematics scores acceptable to the Department or MATH 104F

UL: credit will not be given for MATH 1090 if any of MATH 1000, MATH 1001, the former MATH 1080, or the former MATH 1081 have been completed

2000

Calculus III

is a study of the differential calculus of functions of two variables, an introduction to convergence of infinite sequences and series.

CR: the former Engineering 1411, the former Engineering 1412, the former Engineering 2412, the former Engineering 2413

LH: 1.5

PR: MATH 1001

2050

Linear Algebra I

includes the topics of Euclidean n-space, vector operations in 2- and 3-space, complex numbers, linear transformations on n-space, matrices, determinants, and systems of linear equations.

CR: the former Engineering 2402

PR: A combination of placement test and high school Mathematics scores acceptable to the Department or 3 credit hours in first year Mathematics courses.

2051

Linear Algebra II

includes the topics of real and complex vector spaces, basis, dimension, change of basis, eigenvectors, inner products, and diagonalization of Hermitian matrices.

2090

Mathematics of Finance

covers the following topics: simple and compound interest and discount, forces of interest and discount, equations of value, annuities and perpetuities, amortization schedules and sinking funds, bonds and other securities, contingent payments.

PR: MATH 1001

2130

Technical Writing in Mathematics

is a project oriented course combining mathematical investigation and technical writing. By using computer programming, graphical and typesetting tools, students will explore mathematical concepts and will produce technical reports of professional quality. The latter will combine elements of writing and graphics to convey technical ideas in a clear and concise manner.

PR: MATH 1001 and (Computer Science 1510 or 1710 or 2710 or 2602 or permission of the Head of Department).

2320

Discrete Mathematics

are basic concepts of mathematical reasoning, sets and set operations, functions, relations including equivalence relations and partial orders as illustrated through the notions of congruence and divisibility of integers, mathematical induction, principles of counting, permutations, combinations and the Binomial Theorem.

CR: the former Computer Science 2740

2500

Statistics for Business and Arts Students

is descriptive statistics (including histograms, stem-and-leaf plots and box plots), elementary probability, random variables, the binomial distribution, the normal distribution, sampling distribution, estimation and hypothesis testing including both one and two sample tests, paired comparisons, correlation and regression, related applications.

CR: STAT 2550, the former STAT 2510, Psychology 2910, Psychology 2925 and the former Psychology 2900

LH: 1.5

PR: MATH 1000 or 6 credit hours in first year courses in Mathematics or registration in at least semester 3 of a Bachelor of Nursing program or permission of the Head of Department.

2550

Statistics for Science Students

is an introduction to basic statistics methods with an emphasis on applications to the sciences. Material includes descriptive statistics, elementary probability, binomial distribution, Poisson distribution, normal distribution, sampling distribution, estimation and hypothesis testing (both one and two sample cases), chi-square test, one way analysis of variance, correlation and simple linear regression.

CR: Engineering 4421, STAT 2500, the former STAT 2510, Psychology 2910, Psychology 2925 and the former Psychology 2900.

LH: 1.5

OR: Statistical computer package will be used in the laboratory, but no prior computing experience is assumed

PR: MATH 1000 or the former MATH 1081

3000

Real Analysis I

is proof techniques, structure of R, sequences, limits, continuity, uniform continuity, differentiation.

CR: the former MATH 2001

LH: 1

PR: MATH 2000

3132

Numerical Analysis I

includes a discussion of round-off error, the solution of linear systems, iterative methods for nonlinear equations, interpolation and polynomial approximation, least squares approximation, fast Fourier transform, numerical differentiation and integration.

CR: Computer Science 3731

PR: MATH 2000, MATH 2050, and a computing course (Computer Science 1510 is recommended)

3202

Vector Calculus

deals with functions of several variables. Lagrange multipliers, vector valued functions, directional derivatives, gradient, divergence, curl, transformations, Jacobians, inverse and implicit function theorems, multiple integration including change of variables using polar, cylindrical and spherical co-ordinates, Green’s theorem. Stokes’ theorem, divergence theorem, line integrals, arc length.

CR: Physics 3810

3240

Applied Graph Theory

examines algorithms and complexity, definitions and basic properties of graphs, Eulerian and Hamiltonian chains, shortest path problems, graph colouring, planarity, trees, network flows, with emphasis on applications including scheduling problems, tournaments, and facilities design.

CR: the former Computer Science 2741

PR: MATH 2320

3260

Ordinary Differential Equations I

is direction fields, equations of first order and first degree, higher order linear equations, variation of parameters, methods of undetermined coefficients, Laplace transforms, systems of differential equations. Applications include vibratory motion, satellite and rocket motion, pursuit problems, population models and chemical kinetics.

CR: MATH 2260 or the former Engineering 3411

PR: MATH 2000

3320

Abstract Algebra

is an introduction to groups and group homomorphisms including cyclic groups, cosets, Lagrange's theorem, normal subgroups and quotient groups, introduction to rings and ring homomorphisms including ideals, prime and maximal ideals, quotient rings, integral domains and fields.

PR: MATH 2320

3330

Euclidean Geometry

is classical Euclidean geometry of the triangle and circle. The inversion transformation, including the theorem of Feuerbach. Elliptic and hyperbolic geometries.

CR: MATH 2330

3340

Introductory Combinatorics

includes Topics such as distributions, the binomial and multinomial theorems, Stirling numbers, recurrence relations, generating functions and the inclusion-exclusion principle. Emphasis will be on applications.

PR: MATH 2320

3370

Introductory Number Theory

is perfect numbers and primes, divisibility, Euclidean algorithm, greatest common divisors, primes and the unique factorization theorem, congruences, cryptography (secrecy systems), Euler-Fermat theorems, power residues, primitive roots, arithmetic functions, Diophantine equations, topics above in the setting of the Gaussian integers.

PR: MATH 2320

3410

Mathematical Statistics I

is basic probability concepts, combinatorial analysis, conditional probability, independence, random variable, distribution function, mathematical expectation, Chebyshev's inequality, distribution of two random variables, binomial and related distributions, Poisson, gamma, normal, bivariate normal, t, and F distributions, transformations of variables including the moment-generating function approach.

OR: one and a half hour tutorial period weekly

PR: MATH 2000

4132

Introduction to Optimization

is an introduction to optimization, analytic methods for functions of one variable and for functions of several variables, classical maxima and minima, necessary and sufficient conditions, constrained optimization, equality and inequality constraints, Kuhn-Tucker conditions, introduction to the calculus of variations, linear programming, simplex algorithm.

4160

Partial Differential Equations I

covers two point boundary value problems, Fourier series, Sturm-Liouville theory, canonical forms, classification and solution of linear second order partial differential equations in two independent variables, separation of variable, integral transform methods.

4242

Algorithms and Complexity

is a study of the correctness and complexity of algorithms, with particular focus on algorithms important in mathematics. Topics may include sorting and binary search, string searching, integer multiplication and exponentiation, matrix multiplication, geometric problems such as closest pair of points and convex hull, probabilistic and approximative algorithms. This course discusses polynomial reductions and NP-completeness.

4340

Combinatorial Analysis

continues most of the topics started in 3340 with further work on distributions, recurrence relations and generating functions. Generating functions are used to solve recurrence relations in two variables. Also included is a study of Polya's theorem with applications.

4950

Senior Project

is a course in which, under the guidance of a faculty member, students conduct a scientific study based upon original research or a critical review of extant data in an appropriate area. Normally the project will have a computational component. Students are required to submit a report and give a presentation. This project fulfils the Core requirement for a fourth-year individual project in the area of specialization. This is a Designated Writing Course.

PR: permission of Program Chair