Office of the Registrar
Faculty of Science (2009/2010)
8.8 Mathematics and Statistics

In the descriptions of the courses which follow, the symbol (F) represents the Fall and (W) represents Winter. These labels are intended to indicate the semester when the course is generally offered. Unlabelled courses are offered as demand or programs dictate and as resources permit. The Department tries to offer a variety of 1000-, 2000- and 3000-level courses during the Spring semester (or intersession or Summer session) every year. Students are encouraged to consult the Department regularly for specific planned offerings, semester by semester.

8.8.1 Foundation Courses

102F

Mathematics Skills Program

is 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.

CH: 0

102N

Mathematics Skills Program for the B.N. (Collaborative) Program

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

CH: 0

103F

Mathematics Skills Program

is 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.

CH: 0

PR: Mathematics 102F

104F

Mathematics Skills Program

is 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.

CH: 0

PR: Mathematics 103F

AR = Attendance requirement; CH = Credit hours are 3 unless otherwise noted; CO = Co-requisite(s); CR = Credit can be retained for only one course from the set(s) consisting of the course being described and the course(s) listed; LC = Lecture hours per week are 3 unless otherwise noted; LH = Laboratory hours per week; OR = Other requirements of the course such as tutorials, practical sessions, or seminars; PR = Prerequisite(s); UL = Usage limitation(s).
8.8.2 Accelerated M103F/M1051 Mathematics Skills Program/Finite Mathematics II (W)

103F

Mathematics Skills Program/Finite Mathematics II

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.

CH: 0

CO: Mathematics 102F and a recommendation by an MLC instructor resulting in approval by the MLC Director

LH: three 50 minute classes and two 75 minute classes per week

PR: Mathematics 102F and a recommendation by an MLC instructor resulting in approval by the MLC Director

AR = Attendance requirement; CH = Credit hours are 3 unless otherwise noted; CO = Co-requisite(s); CR = Credit can be retained for only one course from the set(s) consisting of the course being described and the course(s) listed; LC = Lecture hours per week are 3 unless otherwise noted; LH = Laboratory hours per week; OR = Other requirements of the course such as tutorials, practical sessions, or seminars; PR = Prerequisite(s); UL = Usage limitation(s).
8.8.3 Common Core Mathematics Courses

Mathematics courses are designated by MATH.

1000

Calculus I

(F) & (W)

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

CR: the former 1081

LC: 4

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

1001

Calculus II

(F) & (W)

is an introduction to integral Calculus with applications.

CR: the former Engineering 1411 or the former Engineering 2413

LH: one and one-half hour problem lab

PR: MATH 1000 or the former 1081

1031

Mathematical Problem Solving

- inactive course.

1050

Finite Mathematics I

(F) & (W)

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

CR: the former MATH 1150

LC: 4

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

UL: 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.

1051

Finite Mathematics II

(F) & (W)

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

CR: the former MATH 1151

LC: 4

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

UL: 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.

1090

Algebra and Trigonometry

(F) & (W)

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: if previously completed or currently registered for MATH 1000, 1001, the former 1080, or the former 1081

LC: 4

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

2000

Calculus III

(F) & (W)

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, 1412, 2412, or 2413

LH: one and one-half hour problem lab

PR: MATH 1001

2050

Linear Algebra I

(F) & (W)

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.

CR: the former Engineering 2402

PR: MATH 1000 or 6 credit hours in first year Mathematics courses

2051

Linear Algebra II

(F) & (W)

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

PR: MATH 2050

2075

Introduction to the History of Mathematics

- inactive course.

2090

Mathematics of Finance

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.

PR: MATH 1001

2091

Introduction to Actuarial Mathematics

- inactive course.

3000

Real Analysis I

(F) & (W)

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

CR: the former MATH 2001

LH: 1

PR: MATH 2000

3001

Real Analysis II

(F) & (W)

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

CR: the former Applied Mathematics 3201 and Pure Mathematics 3201

LH: 1

PR: MATH 3000

4000

Lebesgue Integration

(F)

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.

CR: the former Pure Mathematics 4400

PR: MATH 3001

4001

Functional Analysis

(W)

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.

CR: the former Pure Mathematics 4302

PR: MATH 3001

AR = Attendance requirement; CH = Credit hours are 3 unless otherwise noted; CO = Co-requisite(s); CR = Credit can be retained for only one course from the set(s) consisting of the course being described and the course(s) listed; LC = Lecture hours per week are 3 unless otherwise noted; LH = Laboratory hours per week; OR = Other requirements of the course such as tutorials, practical sessions, or seminars; PR = Prerequisite(s); UL = Usage limitation(s).
8.8.4 Applied Mathematics Courses

Applied Mathematics courses are designated by AMAT.

2130

Technical Writing in Mathematics

(W)

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: admission to Applied or Pure Mathematics major and Mathematics 1001 and (Computer Science 1510 or 1710 or 2710 or 2602; or permission of the Head of Department)

UL: qualifies as a Research/Writing course in the Faculty of Arts

3100

Introduction to Dynamical Systems

(W)

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

CR: the former AMAT 3190

PR: AMAT 3260 or Pure Mathematics 3260

3111

Applied Complex Analysis

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.

PR: AMAT 3210 or Pure Mathematics 3210

3132

Numerical Analysis I

(W)

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.

CR: Computer Science 3731

PR: Mathematics 3000 or AMAT 3260 or Pure Mathematics 3260, and a computing course (Computer Science 1510 is recommended).

3161

Ordinary Differential Equations II

(F)

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.

PR: AMAT 3202 or Pure Mathematics 3202 and AMAT 3260 or Pure Mathematics 3260

3202

Vector Calculus

(F) & (W)

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: AMAT 3202 or Pure Mathematics 3202, Physics 3810

PR: Mathematics 2000 and 2050

3210

Introduction to Complex Analysis

(F)

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.

CR: Pure Mathematics 3210

PR: Mathematics 3000

3240

Applied Graph Theory

(F)

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, Pure Mathematics 3240

PR: Pure Mathematics 2320

3260

Ordinary Differential Equations I

(F) & (W)

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.

CR: AMAT 3260 or Pure Mathematics 3260, the former Engineering 3411

PR: Mathematics 2000

4100

Applied Functional Analysis

- inactive course.

4102

Stochastic Methods in Applied Mathematics

- inactive course.

4130

Introduction to General Relativity

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.

CO: AMAT 4230 or Pure Mathematics 4230

CR: Physics 4220

PR: AMAT 3202 or Pure Mathematics 3202 and one of Physics 3220, AMAT 4230 or Pure Mathematics 4230 or permission of the Head of Department.

4131

Numerical Linear Algebra

- inactive course.

4132

Introduction to Optimization

- inactive course.

4133

Numerical Optimization

- inactive course.

4140

Introduction to Mathematical Control Theory

- inactive course.

4160

Partial Differential Equations I

(F)

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.

PR: AMAT 3202 or Pure Mathematics 3202 and AMAT 3260 or Pure Mathematics 3260

4161

Integral Equations

- inactive course.

4162

Numerical Methods for Partial Differential Equations

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

PR: AMAT 3132, 4160

4170

Partial Differential Equations II

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.

PR: AMAT 4160

4180

Introduction to Fluid Dynamics

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.

CR: Physics 4205

PR: Physics 3220 and either AMAT 4160 or Physics 3821

4190

Mathematical Modelling

(W)

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.

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

419A and 419B

Applied Mathematics Honours Project

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.

CH: 6

CR: the former AMAT 4199

PR: registration in an Honours or Joint Honours program in Applied Mathematics.

4230

Differential Geometry

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.

CR: Pure Mathematics 4230

PR: AMAT 3202 or Pure Mathematics 3202

4240

Differential and Integral Calculus on Manifolds

- inactive course.

4280-4290

Special Topics in Pure and Applied Mathematics

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

PR: permission of the Head of the Department

AR = Attendance requirement; CH = Credit hours are 3 unless otherwise noted; CO = Co-requisite(s); CR = Credit can be retained for only one course from the set(s) consisting of the course being described and the course(s) listed; LC = Lecture hours per week are 3 unless otherwise noted; LH = Laboratory hours per week; OR = Other requirements of the course such as tutorials, practical sessions, or seminars; PR = Prerequisite(s); UL = Usage limitation(s).
8.8.5 Pure Mathematics Courses

Pure Mathematics courses are designated by PMAT.

2320

Discrete Mathematics

(F) & (W)

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.

CR: the former Computer Science 2740

PR: Mathematics 1001 or 2050

3202

Vector Calculus

(F) & (W)

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, Applied Mathematics 3202

PR: Mathematics 2000 and 2050

3210

Introduction to Complex Analysis

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.

CR: Applied Mathematics 3210

PR: Mathematics 3000

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, Applied Mathematics 3240

PR: PMAT 2320

3260

Ordinary Differential Equations I

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.

CR: the former Engineering 3411, Applied Mathematics 3260

PR: Mathematics 2000

3300

Set Theory

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.

PR: PMAT 2320

3303

Introductory Geometric Topology

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.

PR: PMAT 2320

3320

Abstract Algebra

(F)

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: PMAT 2320

3321

Applied Algebra

- inactive course.

3330

Euclidean Geometry

(F)

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

PR: PMAT 2320 or Mathematics 2051

3331

Projective Geometry

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

PR: PMAT 2320 or Mathematics 2051

3340

Introductory Combinatorics

(W)

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

PR: PMAT 2320

3370

Introductory Number Theory

(F)

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.

PR: PMAT 2320

3410

Mathematical Statistics I

(F)

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.

CR: Statistics 3410

OR: one and a half hour tutorial period weekly

PR: Mathematics 2000

3411

Mathematical Statistics II

(W)

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.

CR: Statistics 3411

OR: one and a half hour tutorial period weekly

PR: PMAT 3410 or Statistics 3410

4230

Differential Geometry

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.

CR: Applied Mathematics 4230

PR: Applied Mathematics 3202 or PMAT 3202

4240

Differential and Integral Calculus on Manifolds

covers definition and properties of differential manifolds, differentiable maps, tangent spaces, differential of a map, rank of a map, submersion, immersion, submanifolds, Lie group and algebra, one-parameter subgroups, exponential map, canonical co-ordinates, adjoint representation, Lie transformation groups, homogeneous spaces of Lie groups, fibre bundles.

CR: Applied Mathematics 4240

PR: Applied Mathematics 4230 or PMAT 4230

4280-4290

Special Topics in Pure and Applied Mathematics

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

PR: permission of the Head of the Department

4300

General Topology

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.

PR: PMAT 3300 or both Mathematics 3000 and PMAT 3303

4301

Algebraic Topology

- inactive course.

4310

Complex Function Theory

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.

PR: Applied Mathematics 3210 or PMAT 3210

4320

Ring Theory

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.

PR: PMAT 3320

4321

Group Theory

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

PR: PMAT 3320

4331

Galois Theory

- inactive course.

4340

Combinatorial Analysis

continues most of the topics started in PMAT 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.

PR: Mathematics 2000 and PMAT 3340

4341

Combinatorial Designs

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

PR: PMAT 3320 or 3340

4370

Number Theory

- inactive course.

4375

History of Mathematics

- inactive course.

4399

Pure Mathematics Dissertation

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.

PR: registration in an Honours or Joint Honours program in Pure Mathematics

4401

Probability Theory

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

CR: Statistics 4401

PR: Mathematics 3000, PMAT 3410 or Statistics 3410

4402

Stochastic Processes

- inactive course.

4410

Mathematical Statistics III

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

CR: Statistics 4410

PR: Mathematics 2051, PMAT 3411 or Statistics 3411

AR = Attendance requirement; CH = Credit hours are 3 unless otherwise noted; CO = Co-requisite(s); CR = Credit can be retained for only one course from the set(s) consisting of the course being described and the course(s) listed; LC = Lecture hours per week are 3 unless otherwise noted; LH = Laboratory hours per week; OR = Other requirements of the course such as tutorials, practical sessions, or seminars; PR = Prerequisite(s); UL = Usage limitation(s).
8.8.6 Statistics Courses

Statistics courses are designated by STAT.

2500

Statistics for Business and Arts Students

(F) & (W)

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.

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

LH: one 90 minute lab per week. Statistical computer package will be use in the laboratory, but no prior computing experience is assumed.

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

2501

Further Statistics for Business and Arts Students

(F)

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

CR: STAT 2560, the former 2511, Psychology 2911, 2950, and the former 2901

LH: one 90 minute lab per week. Statistical computer package will be used in the laboratory.

PR: STAT 2500 or 2510

2510

Statistics for Physical Science Students

(F) & (W)

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.

CR: STAT 2500, 2550, Psychology 2910, 2925, the former 2900, the former Engineering 3423 and 4421

LH: one 90 minute lab per week

PR: Mathematics 1000 or the former 1081

2550

Statistics for Life Science Students

(F) & (W) & (S)

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.

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

LH: one 90 minute lab per week. Statistical computer package will be used in the laboratory, but no prior computing experience is assumed.

PR: Mathematics 1000 or the former 1081

2560

Further Statistics for Science Students

(W)

(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.

CR: STAT 2501, the former 2511, Psychology 2911, 2950, and the former 2901

LH: one 90 minute lab per week. Statistical computer packages will be used in the laboratory, but no prior computing experienced is assumed.

PR: STAT 2500 (with Mathematics 1000 or the former 1081) or STAT 2510

3410

Mathematical Statistics I

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.

CR: Pure Mathematics 3410

OR: one and a half hour tutorial period weekly

PR: Mathematics 2000

3411

Mathematical Statistics II

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.

CR: Pure Mathematics 3411

OR: one and a half hour tutorial period weekly

PR: Pure Mathematics 3410 or STAT 3410

3520

Experimental Design I

(F)

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.

CR: Psychology 3900 and 3950

PR: Mathematics 2050 and either Pure Mathematics 3411 or STAT 3411 or both 1001 and one of STAT 2501 or 2560 or the former 2511

3521

Regression

(W)

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.

PR: Mathematics 2050 and either Pure Mathematics 3411 or STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511

3530

Survey Sampling I

(F)

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.

PR: either Pure Mathematics 3411 or STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511

3540

Time Series I

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.

PR: either Pure Mathematics/STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511

3570

Reliability and Quality Control

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.

PR: either Pure Mathematics 3411 or STAT 3411 or both Mathematics 1001 and one of STAT 2501 or 2560 or the former 2511

3590

Statistics in Applied Research

- inactive course.

4401

Probability Theory

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.

CR: Pure Mathematics 4401

PR: Mathematics 3000, Pure Mathematics 3410 or STAT 3410

4402

Stochastic Processes

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

CR: Applied Mathematics 4102, Pure Mathematics 4402

PR: Pure Mathematics 3410 or STAT 3410

4410

Mathematical Statistics III

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

CR: Pure Mathematics 4410

PR: Mathematics 2051, Pure Mathematics 3411 or STAT 3411

4520

Experimental Design II

(W)

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

PR: STAT 3520

4530

Survey Sampling II

(W)

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.

PR: Mathematics 2000 and STAT 3530

4540

Time Series II

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.

PR: Pure Mathematics 3411 or STAT 3411 and STAT 3540

4550

Non-parametric Statistics

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.

PR: one of STAT 3520 or 3521, or Pure Mathematics 3411 or STAT 3411

4560

Continuous Multivariate Analysis

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.

PR: Mathematics 2051, Pure Mathematics 3410 or STAT 3410 and one of STAT 3520, or Pure Mathematics 3411 or STAT 3411, or STAT 3521

4561

Discrete Multivariate Analysis

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.

PR: STAT 3520 or 3521

4580

History of Statistics

- inactive course.

4581

Quantitative Methods in Biology

- inactive course.

4585

Computational Statistics

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.

PR: Mathematics 2000, STAT 3520, 3521. Applied Mathematics 2130 or the former Pure Mathematics 2130 is recommended

4590

Statistical Analysis of Data I

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.

LH: one 90 minute lab per week

PR: one of STAT 3520, or 3521, or Pure Mathematics 3411 or STAT 3411

4591

Statistical Analysis of Data II

- inactive course.

4599

Honours Comprehensive with Directed Readings

is a directed reading course with Comprehensive examination.

PR: registration in an Honours or Joint Honours program in Statistics

AR = Attendance requirement; CH = Credit hours are 3 unless otherwise noted; CO = Co-requisite(s); CR = Credit can be retained for only one course from the set(s) consisting of the course being described and the course(s) listed; LC = Lecture hours per week are 3 unless otherwise noted; LH = Laboratory hours per week; OR = Other requirements of the course such as tutorials, practical sessions, or seminars; PR = Prerequisite(s); UL = Usage limitation(s).