is a non-credit course intended for students who either have a weak background in mathematics or are returning to the subject after some years. The course enables students to master mathematical operations such as those involving whole numbers, fractions, decimals, percents, integers, exponents, linear equations and algebraic expressions.

is a non-credit course intended for students of the B.N. (Collaborative) Program who have a weak background in mathematics and/or have not done mathematics in some years. The course enables students to master mathematical operations such as those involving whole numbers, fractions, decimals, percents, units of measurement, ratios and proportions.

is non-credit course intended for students who either have a weak background in mathematics or are returning to the subject after some years. The course enables students to master mathematical operations such as those involving rational expressions and equations, units of measurement, ratios and proportions, formulas, graphs of linear equations, systems of linear equations, basic geometry and trigonometry and number systems.

is a non-credit course intended for those students who either have a weak background in mathematics or are returning to the subject after some years. The course enables students to master mathematical operations such as those involving number systems, algebraic and rational expressions, linear and rational equations, formulas, exponents, radicals, quadratic equations and logarithms.

is 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. Mathematics 1051 is a credit course with topics including elementary matrices, linear programming, elementary number theory, mathematical systems and geometry.

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

is an introduction to integral Calculus with applications.

- inactive course.

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

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

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.

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

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.

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

- 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.

- inactive course.

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.

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.

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

covers graphs and the four colour problem, orientable and non-orientable surfaces, triangulation, Euler characteristic, classification and colouring of compact surfaces, basic point-set topology, the fundamental group, including the fundamental groups of surfaces, knots, and the Wirtinger presentation of the knot group.

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.

- inactive course.

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

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

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

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.

includes a review of the Riemann integral, functions of bounded variation, null sets and Lebesgue measure, the Cantor set, measurable sets and functions, the Lebesgue integral in R1 and R2, Fatou's lemma, Monotone and Dominated Convergence Theorems, Fubini's Theorem, an introduction to Lebesgue-Stieltjes measure and integration.

includes metric and normed spaces, completeness, examples of Banach spaces and complete metric spaces, bounded linear operators and their spectra, bounded linear functionals and conjugate spaces, the fundamental theorems for Banach spaces including the Hahn–Banach Theorem, topology including weak and weak* topologies, introduction to Hilbert spaces.

- 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.

- 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.

- inactive course.

covers numerical solution of initial value problems for ordinary differential equations by single and multi-step methods, Runge-Kutta, and predictor-corrector; numerical solution of boundary value problems for ordinary differential equations by shooting methods, finite differences and spectral methods; numerical solution of partial differential equations by the method of lines, finite differences, finite volumes and finite elements.

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.

(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.

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

is a two-semester course that requires the student, with supervision by a member of the Department, to prepare a dissertation in an area of Applied Mathematics. In addition to a written project, a one hour presentation will be given by the student at the end of the second semester.

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.

- inactive course.

will have the topics to be studied announced by the Department. Consult the Department for a list of titles and information regarding availability.

examines topological structure on a set, neighbourhood, 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.

- 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.

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.

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

- inactive course.

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.

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

is continued fractions, an introduction to Diophantine approximations, selected Diophantine equations, the Dirichlet product of arithmetic functions, the quadratic reciprocity law, and factorization in quadratic domains.

- 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.

examines the basic statistical issues encountered in everyday life, such as data collection (both primary and secondary), ethical issues, planning and conducting statistically-designed experiments, understanding the measurement process, data summarization, measures of central tendency and dispersion, basic concepts of probability, understanding sampling distributions, the central limit theorem based on simulations (without proof), linear regression, concepts of confidence intervals and testing of hypotheses. Statistical software will be used to demonstrate each technique.

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.

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

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. This course is normally offered twice a year, including the Fall.

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.

(formerly STAT 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.

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.

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.

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.

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.

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.

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.

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.

- inactive course.

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.

covers stochastic processes, stationarity, random walks, Markov chains, renewal, and queuing.

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

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

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.

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.

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.

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.

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.

- 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.

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.

- inactive course.

is a directed reading course with Comprehensive examination.