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.

A non-credit course enabling students to master mathematics operations such as those involving algebraic and rational expressions, formulas, graphs, systems of linear equations, basic trigonometry and number systems. / 1051 is a credit course with topics including elementary matrices, linear programming, elementary number theory, mathematical systems and geometry. Meets for three 50 minute classes and two 75 minute classes per week.

Prerequisites/Co-requisites: Mathematics 102F and a recommendation by an MLC instructor resulting in approval by the MLC Director.

is an introduction to differential Calculus including logarithmic, exponential and trigonometric functions.

Four hours per week.

Prerequisite: Mathematics 1090 or a combination of placement test and high school Mathematics scores acceptable to the department.

is an introduction to integral Calculus with applications. In addition to three lectures per week there will be a one and one-half hour problem lab.

Prerequisite: Mathematics 1000 or 1081.

- inactive course.

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

Four hours per week.

Prerequisite: A combination of placement test and high school mathematics scores acceptable to the department or Mathematics 103F.

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

Four hours per week.

Prerequisite: A combination of placement test and high school mathematics scores acceptable to the department or Mathematics 103F.

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.

Four hours per week.

Prerequisite: A combination of placement test and high school Mathematics scores acceptable to the department or Mathematics 104F.

is a study of the differential calculus of functions of two variables, an introduction to convergence of infinite sequences and series. In addition to three lectures per week there will be a one and one-half hour problem lab.

Prerequisite: Mathematics 1001.

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

Prerequisite: Mathematics 1000 or six credit hours in first year Mathematics courses.

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

Prerequisite: Mathematics 2050.

- inactive course.

covers the 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.

Prerequisite: Mathematics 1001.

- inactive course.

covers proof techniques, structure of the real numbers, sequences, limits, continuity, uniform continuity, differentiation.

Three lecture hours and one laboratory hour per week.

Prerequisite: Mathematics 2000.

examines Infinite series of constants, sequences and series of functions, uniform convergence and its consequences, power series, Taylor series, Weierstrass Approximation Theorem.

Three lecture hours and one laboratory hour per week.

Prerequisite: Mathematics 3000.

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.

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

examines flows, stability, phase plane analysis, limit cycles, bifurcations, chaos, attractors, maps, fractals. Applications throughout.

Three lecture hours per week.

Prerequisite: Applied Mathematics/Pure Mathematics 3260.

examines mapping by elementary functions, conformal mapping, applications of conformal mapping, Schwartz-Christoffel transformation, Poisson integral formula, poles and zeros, Laplace transforms and stability of systems, analytic continuation.

Prerequisite: Applied Mathematics/Pure Mathematics 3210.

is an introduction to numerical analysis, round-off error, iterative methods for nonlinear equations in one variable, interpolation and polynomial approximation, discrete least-squares approximation, numerical differentiation and integration.

Prerequisites: Mathematics 3000 or Applied Mathematics/Pure Mathematics 3260, and a computing course (Computer Science 1510 is recommended).

examines power series solutions, method of Frobenius, Bessel functions, Legendre polynomials and others from classical Physics, systems of linear first order equations, fundamental matrix solution, numerical methods for initial value problems, existence and uniqueness of solutions.

Prerequisites: Applied Mathematics/Pure Mathematics 3202 and Applied Mathematics/Pure Mathematics 3260.

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.

Prerequisite: Mathematics 2000 and 2050.

examines complex numbers, analytic functions of a complex variable, differentiation of complex functions and the Cauchy-Riemann equations, complex integration, Cauchy's theorem, Taylor and Laurent series, residue theory and applications.

Prerequisite: Mathematics 3000.

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

Prerequisite: Pure Mathematics 2320.

examines 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.

Prerequisite: Mathematics 2000.

- inactive course.

- inactive course.

(same as Physics 4220) studies both the mathematical structure and physical content of Einstein’s theory of gravity. Topics include the geometric formulation of special relativity, curved spacetimes, metrics, geodesics, causal structure, gravity as spacetime curvature, the weak-field limit, geometry outside a spherical star, Schwarzschild and Kerr black holes, Robertson-Walker cosmologies, gravitational waves, an instruction to tensor calculus, Einstein’s equations, and the stress-energy tensor.

Prerequisites: Applied Mathematics/Pure Mathematics 3202 and one of Physics 3220, Applied Mathematics/Pure Mathematics 4230 or permission of the Head of Department. Applied Mathematics/Pure Mathematics 4230 may be taken concurrently.

- inactive course.

- inactive course.

- inactive course.

- inactive course.

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.

Prerequisites: Applied Mathematics/Pure Mathematics 3202 and Applied Mathematics/Pure Mathematics 3260.

- inactive course.

cover finite differences, finite elements, discretization schemes, stability analysis. Application to parabolic, elliptic and hyperbolic problems.

Prerequisite: Applied Mathematics 3132, 4160.

covers first order equations, Cauchy problems, Cauchy-Kowalewska theorem, second order equations, canonical forms, wave equations in higher dimensions, method of spherical means, Duhamel's principle, potential equation, Dirichlet and Neuman problem, Green's function and fundamental solution, potential theory, heat equation, Riemann's method of integration, method of plane and Riemann waves for systems of PDEs of the first order.

Prerequisite: Applied Mathematics 4160.

(same as Physics 4205) covers basic observations, mass conservation, vorticity, stress, hydrostatics, rate of strain, momentum conservation (Navier-Stokes equation), simple viscous and inviscid flows, Reynolds number, boundary layers, Bernoulli's and Kelvin's theorems, potential flows, water waves, thermodynamics.

Prerequisites: Physics 3220 and either Applied Mathematics 4160 or Physics 3821.

is intended to develop students' skills in mathematical modelling and competence in oral and written presentations. Case studies in modelling will be analyzed. Students will develop a mathematical model and present it in both oral and report form.

Prerequisites: Applied Mathematics 3100, Applied Mathematics 3161, Applied Mathematics 4160, and a technical writing course offered by a Science department (Applied Mathematics 2130 is recommended).

requires the student, with supervision by a member of the department, to prepare a dissertation in an area of Applied Mathematics. Although original research work by the student will not normally be expected, the student must show an ability and interest to learn and organize material independently. A one hour presentation at the end of the semester will be given by the student.

Prerequisite: Registration in an Honours or Joint Honours program in Applied Mathematics.

covers theory of curves, Frenet relations, curvature and torsion, singular points of curves, first and second quadratic forms, classification of points on a surface, Gaussian curvature, Gauss-Weingarten theorem, Christoffel's symbols, theorema Egregium, Gauss-Cadazzi-Mainardi theorem, internal geometry of surfaces, isometric and conformal mappings, geodesic curvature and torsion, parallel displacement, Gauss-Bonnet theorem.

Prerequisite: Applied Mathematics/Pure Mathematics 3202.

- inactive course.

Prerequisite: Permission of Head of Department.

covers 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.

Prerequisite: Mathematics 1001 or 2050.

see Applied Mathematics 3202.

see Applied Mathematics 3210.

see Applied Mathematics 3240.

see Applied Mathematics 3260.

is an introduction to Mathematical Logic, functions, equivalence relations, equipotence of sets, finite and infinite sets, countable and uncountable sets, Cantor's Theorem, Schroeder-Bernstein Theorem, ordered sets, introduction to cardinal and ordinal numbers, logical paradoxes, the axiom of choice.

Prerequisite: Pure Mathematics 2320.

is a brief review of the Riemann integral, Riemann-Stieltjes integration, metric spaces, the Baire Category Theorem, uniform continuity, the Banach Contraction principle, the Weierstrass Approximation Theorem and the Stone-Weierstrass Theorem are covered.

Prerequisite: Mathematics 3001.

- inactive course.

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.

Prerequisite: Pure Mathematics 2320.

- inactive course.

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

Prerequisite: Pure Mathematics 2320 or Mathematics 2051.

includes course topics: projective space, the principle of duality, mappings in projective space, conics and quadrics.

Prerequisite: Pure Mathematics 2320 or Mathematics 2051.

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

Prerequisite: Pure Mathematics 2320.

examines 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.

Prerequisite: Pure Mathematics 2320.

covers 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.

One and a half hour tutorial period weekly.

Prerequisite: Mathematics 2000.

examines sampling distributions. Limiting distributions, central limit theorem, minimum variance unbiased estimators, confidence intervals, MLE and its asymptotic properties, exponential family, sufficient statistics, Rao-Cramér inequality, efficiency, Neyman-Pearson lemma, chi-square tests, likelihood ratio test.

One and a half hour tutorial period weekly.

Prerequisite: Pure Mathematics/Statistics 3410.

see Applied Mathematics 4230.

see Applied Mathematics 4240.

Prerequisite: Permission of Head of Department.

examines topological structure on a set, neighborhood, open and closed sets, continuity, sub-spaces and quotient spaces, connectedness, relation between topologies, base and sub-base, product spaces, applications to Euclidean spaces. Hausdorff, regular, normal and compact spaces, metric spaces, compacta and continua, metrizability.

Prerequisite: Pure Mathematics 3300 or 3301, or both Mathematics 3000 and Pure Mathematics 3303.

- inactive course.

- inactive course.

examines topology of C, analytic functions, Cauchy's theorem with proof, Cauchy integral formula, singularities, argument principle, Rouche's theorem, maximum modulus principle, Schwarz's lemma, harmonic functions, Poisson integral formula, analytic continuation, entire functions, gamma function, Riemann-Zeta function, conformal mapping.

Prerequisite: Pure Mathematics 3301 and Applied Mathematics/Pure Mathematics 3210.

examines factorization in integral domains, structure of finitely generated modules over a principal ideal domain with application to Abelian groups, nilpotent ideals and idempotents, chain conditions, the Wedderburn-Artin theorem.

Prerequisite: Pure Mathematics 3320.

examines permutation groups, Sylow theorems, normal series, solvable groups, solvability of polynomials by radicals, introduction to group representations.

Prerequisite: Pure Mathematics 3320.

- inactive course.

continues most of the topics started in Pure Mathematics 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.

Prerequisite: Mathematics 2000 and Pure Mathematics 3340.

includes the study of finite fields, Latin squares, finite projective planes and balanced incomplete block designs.

Prerequisite: Pure Mathematics 3320 or 3340.

- inactive course.

- inactive course.

requires the student, with supervision by a member of the department, to prepare a dissertation in an area of Pure Mathematics. Although original research by the student will not normally be expected, the student must show an ability and interest to learn and organize material independently. A one hour presentation at the end of the semester will be given by the student.

Prerequisite: Registration in an Honours or Joint Honours program in Pure Mathematics.

is a review of Riemann integration, outer measure, measure, measurable sets, measurable functions, the Lebesgue integral, properties of the Lebesgue integral, sequences of integrals, Fubini's theorem.

Prerequisite: Mathematics 3001.

examines abstract measure and integration, probability concepts, random variables, independence, Borel-Cantelli lemmas, sums of independent random variables.

Prerequisite: Mathematics 3000 and Pure Mathematics/Statistics 3410.

- inactive course.

examines multivariate normal distribution theory, applications to ANOVA and regression, other topics such as sequential tests, distribution of order statistics, nonparametrics and decision theory.

Prerequisite: Mathematics 2051 and Pure Mathematics/Statistics 3411.

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

Prerequisite: Mathematics 1000 or 6 credit hours in first year courses in Mathematics or registration in at least semester 3 of a B.N. program or permission of the head of department.

coves power calculation and sample size determination, analysis of variance, multiple regression, nonparametric statistics, index numbers, time series analysis, introduction to sampling techniques.

Prerequisite: Statistics 2500 or 2510.

examines elements of probability, conditional probability, Bayes' Theorem, discrete random variables, cumulative distribution function, introduction to continuous random variables, mathematical expectation, estimation of mean, proportion and variance, hypothesis testing for one-sample case.

Prerequisite: Mathematics 1000 or 1081.

is an introduction to basic statistics methods with an emphasis on applications to life sciences and, in particular, to biology. Material includes descriptive statistics, elementary probability, binomial 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.

Prerequisite: Mathematics 1000 or 1081.

(formerly 2511) covers estimation and hypothesis testing in the two-sample and paired sample cases, one way and two way analysis of variance, simple and multiple linear regression, chi-square tests, non-parametric tests including sign test, Wilcoxon signed rank test and Wilcoxon rank test.

Prerequisite: Statistics 2500 (with Mathematics 1000 or 1081) or Statistics 2510.

see Pure Mathematics 3410

see Pure Mathematics 3411

is an introduction to basic concepts in experimental design, single factor designs including completely randomized, randomized blocks, Latin square and related designs, multiple comparison tests, fixed and random effects models, introduction to factorial design.

Prerequisites: Mathematics 2050 and either Pure Mathematics/Statistics 3411 or both 1001 and one of Statistics 2501 or 2560 (former 2511).

covers inferences in linear regression analysis, matrix approach to regression analysis, multiple linear regression, model selection, polynomial regression, indicator variable, problem of simultaneous inferences, multicollinearity.

Prerequisites: Mathematics 2050 and either Pure Mathematics/Statistics 3411 or both Mathematics 1001 and one of Statistics 2501 or 2560 or the former 2511.

covers basic concepts, randomization, sampling frames, stratified sampling, the analysis of subclasses, cluster sampling, stratified cluster sampling, unequal clusters, ratio estimates selection with probabilities proportional to size.

Prerequisites: Either Pure Mathematics/Statistics 3411 or both Mathematics 1001 and one of Statistics 2501 or 2560 or the former 2511.

covers Autocovariance, autocorrelation and correlation, stationarity, autoregressive, moving average and ARMA models, differencing, the integrated ARMA process, parameter estimation, model identification and diagnostic testing, forecasting, seasonal models, the use of data transformation.

Prerequisites: Either Pure Mathematics/Statistics 3411 or both Mathematics 1001 and one of Statistics 2501 or 2560 or the former 2511.

is an analysis of life, mortality and failure data, standard parametric models in reliability, quality control charts and cumulative sum charts, tolerance limits, contingency tables, interactions, application of sequential sampling.

Prerequisites: Either Pure Mathematics/Statistics 3411 or both Mathematics 1001 and one of Statistics 2501 or 2560 or the former 2511.

- inactive course.

see Pure Mathematics 4400

see Pure Mathematics 4401

see Pure Mathematics 4402

see Pure Mathematics 4410

covers selected topics in ANOVA and ANCOVA including factorial experiments and unbalanced designs.

Prerequisite: Statistics 3520.

covers area sampling, multi-stage sampling, two-phase sampling, ratio, regression and difference estimates, composite sampling designs, sampling from imperfect frames, bias and non-sampling errors.

Prerequisites: Mathematics 2000 and Statistics 3530.

is an analysis of time series in the time domain, including stationary and non-stationary processes, autocovariance kernels and their estimators, analysis of autoregressive and moving average models, spectral analysis including the power spectrum and its estimators, periodogram, smoothed and filtered estimators.

Prerequisites: Pure Mathematics/Statistics 3411 and Statistics 3540.

covers inferences concerning location based on one sample, paired samples or two samples, inferences concerning scale parameters, goodness-of-fit tests, association analysis, tests for randomness.

Prerequisites: one of Statistics 3520 or 3521, or Pure Mathematics/Statistics 3411.

examines the multivariate normal distribution and its marginal and conditional distributions, properties of the Wishart distribution, Hotelling's T-squared statistic, a selection of techniques chosen from among MANOVA, multivariate regression, principal components, factor analysis, discrimination and classification, clustering.

Prerequisites: Mathematics 2051, Pure Mathematics/Statistics 3410 and one of Statistics 3520, or Pure Mathematics/Statistics 3411, or Statistics 3521.

is an analysis of cross-classified categorical data, chi-square test, measures of association, multidimensional contingency tables, hypotheses of partial and conditional independence, log-linear models for Poisson, multinomial and product-multinomial sampling schemes, iterative scaling technique for maximum likelihood estimation, step-wise model selection procedures, partitioning chi-square, explanatory and response variables in contingency tables, logit models.

Prerequisite: Statistics 3520 or 3521.

- inactive course.

- inactive course.

is an introduction to modern computational statistics, using a statistical programming language, such as S-Plus. Emphasis is placed on use of the computer for numerical and graphical exploratory data analysis, and on crafting programs to accomplish specialized statistical procedures.

Prerequisites: Mathematics 2000, Statistics 3520, 3521. Applied Mathematics/Pure Mathematics 2130 is recommended.

is for users of Statistics with emphasis placed on computer analysis of statistical problems drawn from various disciplines, descriptive statistics, analysis of univariate measurement data, chi-square tests, non-parametric tests, basic ANOVA and regression.

Prerequisite: one of Statistics 3520, or 3521, or Pure Mathematics/Statistics 3411.

- inactive course.

is a directed reading course with Comprehensive examination for students in Honours or Joint Honours Degree programs in Statistics only.

Prerequisite: Registration in an Honours or Joint Honours program in Statistics.