** Common Core Mathematics Courses**

All undergraduate courses offered by the Department of Mathematics and Statistics are identified to YEAR by the first digit and to SUBJECT AREA by the second digit as follows:

**First Digit**

1- First Year

2- Second Year

3- Third Year

4- Fourth and Fifth Year

**Second Digit**

0- Common Core

1- Applied Mathematics

2- Applied Mathematics and Pure Mathematics

3- Pure Mathematics

4- Pure Mathematics and Statistics

5- Statistics

**COURSE LIST**

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.

**102F, 103F, and 104F. Mathematics Skills Program.** 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.

**COMMON CORE MATHEMATICS COURSES**

**1000. Calculus I (F)(W).** 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. (See regulation 7)

*NOTE: Effective Winter 2000, the credit restriction between Mathematics 1000 and Mathematics 1080 has been lifted.
However, credit cannot be obtained for both Mathematics 1000 and Mathematics 1081.*

**1001. Calculus II (F)(W).** 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.

*NOTE: Credit cannot be obtained for both M 1001 and either Engineering 1411 or Engineering 2413.*

**1031. Mathematical Problem Solving.** An introduction to the theory and practice of mathematical problem solving. The
course will present and illustrate problem-solving strategies.

Four hours per week.

Prerequisite: Three 1000 level Mathematics credit hours and permission of the department.

**1050. Finite Mathematics I (F)(W).** Topics covered 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 (See
regulation 7), or Mathematics 103F.

*NOTES: 1) With the exception of those already admitted at the time of registration in this course to a B.Ed. program that
requires this course, students who already have obtained credit for six or more Mathematics credit hours numbered 2000
or above are not permitted to register for this course nor can they receive credit for it.*

*2) Credit cannot be obtained for M 1050 and the former Mathematics 1150.*

**1051. Finite Mathematics II (F)(W).** Topics covered 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 (See
regulation 7), or Mathematics 103F.

*NOTES: 1) With the exception of those already admitted at the time of registration in this course to a B.Ed. program that
requires this course, students who already have obtained credit for six or more Mathematics credit hours numbered 2000
or above are not permitted to register for this course nor can they receive credit for it.*

*2) Credit cannot be obtained for M 1051 and the former Mathematics 1151.*

**1090. Algebra and Trigonometry (F)(W).** This course 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 (See
regulation 7) or Mathematics 104F.

*NOTE: Students will not receive credit for Mathematics 1090 if they have previously received credit or are currently
registered for M1000, M1001, M1080, or M1081.*

**2000. Calculus III (F)(W).** 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: M 1001.

*NOTE: Credit cannot be obtained for both M 2000 and any of Engineering 1411, Engineering 1412, Engineering 2412,
Engineering 2413.*

**2001. Introductory Real Analysis (F)(W).** Analysis on the real line, number systems, functions, sequences, limits,
continuity, uniform continuity, differentiation.

Prerequisite: M 2000.

**2050. Linear Algebra I (F)(W).** Topics include Euclidean n-space, vector operations in **R**^{2} and **R**^{3}, complex numbers,
linear transformations on **R**^{n}, matrices, determinants, and systems of linear equations.

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

*NOTE: Credit cannot be obtained for both M 2050 and Engineering 2402.*

**2051. Linear Algebra II (F)(W).** Topics include real and complex vector spaces, basis, dimension, change of basis,
eigenvectors, inner products, and diagonalization of Hermitian matrices.

Prerequisite: M 2050.

**2075. Introduction to the History of Mathematics.** Elementary number theory, primes, modular arithmetic, groups and
fields, applications. Evolution of the number concept. Euclid's elements, Archimedes, Apollonius, Kepler. Regular
polyhedra and polygons, Euler's formula, symmetry. Latin and Euler squares, finite geometries, some applications.

Prerequisite: Mathematics 1001 or at least nine credit hours in other Mathematics or Statistics courses.

**2090. Mathematics of Finance.** Topics covered are: 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: M 1001.

**2091. Introduction to Actuarial Mathematics.** Life tables, life annuities, life insurance, multi-life theory, stationary
population, interest rates as a random variable.

Prerequisites: M 2090 and one of ST 2500, 2510, 2550.

In accordance with Senate's *Policy Regarding Inactive Courses*, courses which have not been offered in the previous three
academic years and which are not scheduled to be offered in the current academic year have been removed from the
following listing. For information about any of these inactive courses, please contact the Head of the Department.

**2120. Introduction to Mathematical Programming (F).** This course serves as an introduction to the use of computers in
mathematics. Algorithm design, structured programming and symbolic computing are the main subject areas treated. The
structured programming, using a high-level computer language such as C, includes floating point arithmetic, data types,
loops, conditional branching, functions, formatted I/O and modularity. The programming in a symbolic environment uses a
package like Maple or Mathematica. All programming focuses on problems related to mathematics.

Prerequisite: M1000 or M1081.

*NOTE: First priority for enrolment in this course is given to students whose majors are in mathematics or statistics. Other
students wishing to register must obtain permission from the head of department. Students enrolled in any program within
the Department of Mathematics and Statistics who have completed or are currently registered for AM2130, Computer
Science 2710 or Computer Science 2602 cannot receive credit for AM/PM 2120.*

**2130.** **Technical Writing in Mathematics (W).** 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.

Prerequisite: M 1001 and (AM 2120 or CS 2710 or CS 2602 or permission of the Head of Department).

*NOTE: First priority for enrolment in this course is given to students who are Applied or Pure Mathematics majors. Other
students wishing to register should direct inquiries to the head of department.*

**3111. Applied Complex Analysis.** 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: AM/PM 3210.

**3132. Numerical Analysis I (W).** 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, initial value problems for ordinary differential equations.

Prerequisites: AM 2130 and AM/PM 3260.

*NOTE: Credit cannot be obtained for both AM 3132 and Computer Science 3731.*

**3161. Ordinary Differential Equations II (F)**. Power series solutions, method of Frobenius, Bessel functions, Legendre
polynomials and others from classical Physics, systems of linear first order equations, fundamental matrix solution,
nonlinear equations and stability, Liapunov's method, existence and uniqueness of solutions.

Prerequisites: AM/PM 3202 and AM/PM 3260.

**3190. Introduction to Mathematical Modelling (W).** A study of how mathematical models are constructed in such
disciplines as ecology and biology, for example, models in population dynamics, genetics, evolution and epidemiology, the
role of hypotheses and the effects of various modelling techniques, continuous, discrete, deterministic and stochastic models.

Prerequisites: AM 2130 and AM/PM 3260. ST 2510 is highly recommended.

**3201. Convergence of Sequences and Series (F).** Infinite series of constants, sequences and series of functions, uniform
convergence, Taylor series, improper integrals.

Prerequisite: M 2001 and M 2050.

**3202. Vector Calculus (F)(W).** 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: Either (I) M 2001 and M 2050 or (ii) M 2000, M 2050 and two of the following Physics courses: P 2053,
P 2054, P 2055, P 2056.

*NOTE: Credit cannot be obtained for both AM/PM3202 and Physics 3810.*

**3210. Introduction to Complex Analysis (F).** 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: M 2001.

**3240. Applied Graph Theory (F). **Algorithms and complexity, definitions and basic properties of graphs, Eulerian and
Hamiltonian chains, shortest path problems, graph coloring, planarity, trees, network flows, emphasis on applications
including scheduling problems, tournaments, and facilities design.

Prerequisite: PM2320.

*NOTE: Credit cannot be obtained for both AM/PM 3260 and Computer Science 2741.*

**3260. Ordinary Differential Equations I (F)(W).** 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: M 2000.

*NOTE: Credit cannot be obtained for both AM/PM 3260 and Engineering 3411.*

**4100. Applied Functional Analysis.** Generalized functions and distributions, normed spaces, convergence, completeness
and equivalent norms, contraction mapping theorem with applications to differential and integral equations, Hilbert space,
Bessel, Parseval and Riesz-Fischer theorems, orthogonal decomposition, functionals in Hilbert space, bounded and
self-adjoint operators, eigenvalue problem, spectral theorem.

Prerequisite: AM 3101 and AM 3111.

**4102. Stochastic Methods in Applied Mathematics.** Random walk, Markov chains, discrete branching processes, Markov
processes in continuous time, homogeneous birth and death processes, queuing processes, applications of stochastic
processes in genetics, epidemiology, population dynamics and diffusion.

Prerequisite: PM/ST 3410 and AM/PM 3260.

*NOTE: Credit cannot be obtained for both AM 4102 and PM/ST 4402.*

**4131. Numerical Linear Algebra.** Direct methods for solving linear systems, iterative techniques in matrix algebra,
numerical solution of systems of nonlinear equations.

Prerequisite: AM 3132.

**4132. Introduction to Optimization.** 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.

Prerequisite: AM/PM 3260 and AM/PM 3202.

**4133. Numerical Optimization.** Numerical methods for functions of one variable, for functions of several variables
including unrestricted search, sequential uniform search, irregular search, non-gradient methods, gradient methods with and
without constraints, geometric programming, selection of other topics from dynamic programming, integer programming,
etc., solution of applied problems by numerical optimization.

Prerequisites: AM 4131 and AM 4132.

**4140. Introduction to Mathematical Control Theory.** Introduction to control theory, matrix solution of linear
uncontrolled and controlled systems, linear control systems, controllability, observability, linear feedback, state observers,
stability, criteria, Nyquist condition, Liapunov theory, stability and control, optimal control, Pontryagin's principle, linear
regulator, solution of applied problems including resource management using optimal control theory.

Prerequisites: M 2051 and AM 3161.

**4160. Partial Differential Equations I (F).** 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: AM/PM 3202 and AM/PM 3260.

**4161. Integral Equations.** Types of integral equations, first and second kind Volterra equations, Volterra equations with
difference kernels, method of Laplace transformation, singular Volterra equations, second kind Fredholm equations,
Fredholm equations with degenerate kernels, Fredholm series, Fredholm theorems, integral equations with symmetric
kernels, Hilbert-Schmidt theorem, first kind Fredholm equations, Hammerstein integral equations.

Prerequisite: AM 4100.

**4162. Numerical Methods for Partial Differential Equations.** Finite differences, finite elements, discretization schemes,
stability analysis. Application to parabolic, elliptic and hyperbolic problems.

Prerequisite: AM 3132, AM 4160.

**4170. Partial Differential Equations II.** 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: AM 4160.

**4180. Introduction to Fluid Dynamics.** (Same as Physics 4205). 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 AM 4160 or Physics 3821.

**4190. Mathematical Modelling (W).** The intent of this course is 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.

Prerequisite: AM 3132, AM 3161, AM 3190, and AM 4160.

**4199. Applied Mathematics Honours Project.** The student, with supervision by a member of the department, will 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.

**4230. Differential Geometry.** 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: AM/PM 3202.

**4240. Differential and Integral Calculus on Manifolds.** 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.

Prerequisite: AM/PM 4230.

**4280-4290. Special Topics in Pure and Applied Mathematics.**

Prerequisite: Permission of Head of Department.

*NOTE: Consult the department for a list of titles and information regarding availability.*

**2320. Discrete Mathematics (F)(W). **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 Theormem.

Prerequisite: M1001 or M2050.

*Note: Credit cannot be obtained for both PM2320 and Computer Science 2740.*

**3201. Convergence of Sequences and Series.** See AM 3201.

**3202. Vector Calculus (F)(W).** See AM 3202.

**3210. Introduction to Complex Analysis.** See AM 3210.

**3240. Applied Graph Theory.** See AM 3240.

**3260. Introduction to Ordinary Differential Equations.** See AM 3260.

**3300. Set Theory.** 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: M 2001.

**3301. Integration and Metric Spaces.** 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: AM/PM 3201.

**3303. Introductory Geometric Topology.** 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.

Prerequisite: PM 2320.

**3320. Abstract Algebra (F).** 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: PM 2320.

**3321. Applied Algebra.** The emphasis is on applications of algebra to other important areas: the construction and
error-correcting capabilities of group codes, Boolean algebras and switching circuits, fast sorting and fast addition,
polynomial rings, the discrete Fourier transform, fast multiplication, finite fields, polynomial and BCH codes.

Prerequisite: PM 3320.

**3330. Euclidean Geometry (F).** Classical Euclidean geometry of the triangle and circle. The inversion transformation,
including the theorem of Feuerbach. Elliptic and hyperbolic geometries.

Prerequisite: PM 2320 or M 2051.

**3331. Projective Geometry.** Course topics include: projective space, the principle of duality, mappings in projective space,
conics and quadrics.

Prerequisite: PM 2320 or M 2051.

**3340. Introductory Combinatorics (W). **Topics include distributions, the binomial and multinomial theorems, Stirling
numbers, recurrence relations, generating functions and the inclusion-exclusion principle. Emphasis will be on applications.

Prerequisite: PM2320.

**3370. Introductory Number Theory (F). **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: PM2320.

**3410. Mathematical Statistics I (F).** 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: M2000.

**3411. Mathematical Statistics II (W).** 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: PM/ST3410.

**4230. Differential Geometry.** See AM 4230.

**4240. Differential and Integral Calculus on Manifolds.** See AM 4240.

**4280-4290. Special Topics in Pure and Applied Mathematics.**

Prerequisite: Permission of Head of Department.

*NOTE: Consult the department for a list of titles and information regarding availability.*

**4300. General Topology.** 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: PM 3300 or PM 3301, or both M 2001 and PM 3303.

**4301. Algebraic Topology.** Categories and functors, algebraic and geometric preliminaries, simplicial homology groups.
Chain complexes, homology theories. Singular homology theory. Cohomology groups. Fundamental group and homotopy groups.

Prerequisite: PM 3320 and PM 4300.

**4302. Functional Analysis.** Banach spaces, dual spaces, Hilbert spaces, linear operators and linear functionals.

Prerequisite: PM 3301.

**4310. Complex Function Theory.** 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: PM 3301 and AM/PM 3210.

**4320. Ring Theory.** 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: PM 3320.

**4321. Group Theory.** Permutation groups, Sylow theorems, normal series, solvable groups, solvability of polynomials by
radicals, introduction to group representations.

Prerequisite: PM 3320.

**4331. Galois Theory.** Irreducible polynomials and field extensions. Galois groups and the solution of equations by radicals.

Prerequisite: M 2051 and PM 3320.

**4340. Combinatorial Analysis.** This course continues most of the topics started in PM 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: M 2000 and PM 3340.

**4341. Combinatorial Designs.** This course includes the study of finite fields, Latin squares, finite projective planes and
balanced incomplete block designs.

Prerequisite: PM 3320 or PM 3340.

**4370. Number Theory.** 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 are covered.

Prerequisite: PM 3370.

**4375. History of Mathematics.** The development of Mathematics from the seventeenth century to the beginning of the
twentieth century as exemplified by the work of mathematicians such as Newton, Euler, Lagrange, Gauss, and Poincare.

Prerequisite: Permission of Head of Department.

**4399. Pure Mathematics Dissertation.** The student, with supervision by a member of the department, will 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.

**4400. Lebesgue Integration.** 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: PM 3201.

**4401. Probability Theory.** Abstract measure and integration, probability concepts, random variables, independence,
Borel-Cantelli lemmas, sums of independent random variables.

Prerequisite: M 2001 and PM/ST 3410.

**4402. Stochastic Processes.** The course covers stochastic processes, stationarity, random walks, Markov chains, renewal,
and queuing.

Prerequisite: PM/ST 3410.

*NOTE: Credit cannot be obtained for both AM 4102 and PM/ST 4402.*

**4410. Mathematical Statistics III.** Multivariate normal distribution theory, applications to ANOVA and regression, other
topics such as sequential tests, distribution of order statistics, nonparametrics and decision theory.

Prerequisite: M 2051 and PM/ST 3411.

In accordance with Senate's *Policy Regarding Inactive Courses*, courses which have not been offered in the previous three
academic years and which are not scheduled to be offered in the current academic year have been removed from the
following listing. For information about any of these inactive courses, please contact the Head of the Department.

*NOTE: All 2000-level statistics courses, ST3410, ST3411, ST4590, and ST4591 have a laboratory period weekly.*

**2500. Statistics for Business and Arts Students.** 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: M1000 or six credit hours in first year courses in Mathematics or registration in at least semester 3 of a B.N.
pro-gramme or permission of the head of department.

*NOTE: Credit can be obtained for only one of ST2500, ST2510, ST2550, and Psychology 2900. Normally offered twice a
year, including the fall. Statistical computer package will be use in the laboratory, but no prior computing experience is
assumed.*

**2501. Further Statistics for Business and Arts Students.** Power calculation and sample size determination, analysis of
variance, multiple regression, nonparametric statistics, index numbers, time series analysis, introduction to sampling techniques.

Prerequisite: ST2500 or ST2510.

*NOTE: Credit can be obtained for only one of ST2501, ST2560, the former ST2511, and Psychology 2901. Statistical
computer package will be used in the laboratory.*

**2510. Statistics for Physical Science Students.** 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: M1000 or M1081.

*NOTE: Credit can be obtained for only one of ST2500, ST2510, ST2550, Psychology 2900, and Engineering 2421.
Normally offered twice a year, including the fall.*

**2550. Statistics for Life Science Students.** 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: M1000 or M1081.

*NOTE: Credit can be obtained for only one of ST2500, ST2510, ST2550, and Psychology 2900. Normally offered twice a
year, including the fall. Statistical computer package will be used in the laboratory, but no prior computing experience is
assumed.*

**2560. (former 2511). Further Statistics for Science Students. **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: ST2500 (with M1000 or M1081) or ST2510.

*NOTE: Credit can be obtained for only one of ST2501, ST2560, the former ST2511, and Psychology 2901. Statistical
computer packages will be used in the laboratory, but no prior computing experienced is assumed.*

**3410. Mathematical Statistics I.** See PM 3410.

**3411. Mathematical Statistics II.** See PM 3411.

**3520. Experimental Design I (F).** 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.

Prerequisite: M 2050 and either PM/ST 3411 or both M 1001 and one of ST 2501 or ST 2560 (former 2511).

*NOTE: Credit cannot be obtained for both ST 3520 and Psychology* *3900.*

**3521. Regression (W).** Inferences in linear regression analysis, matrix approach to regression analysis, multiple linear
regression, model selection, polynomial regression, indicator variable, problem of simultaneous inferences, multicollinearity.

Prerequisite: M 2050 and either PM/ST 3411 or both M 1001 and one of ST 2501 or ST2560 or the former ST2511.

**3530. Survey Sampling I (F).** 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.

Prerequisite: Either PM/ST 3411 or both M 1001 and one of ST 2501 or ST2560 or the former ST2511.

**3540. Time Series I.** 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.

Prerequisite: Either PM/ST 3411 or both M 1001 and one of ST 2501 or ST2560 or the former ST2511.

**3570. Reliability and Quality Control.** 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.

Prerequisite: Either PM/ST 3411 or both M 1001 and one of ST 2501 or ST 2560 or the former ST 2511.

**4400. Lebesgue Integration.** See PM 4400.

**4401. Probability Theory.** See PM 4401.

**4402. Stochastic Processes.** See PM 4402.

**4410. Mathematical Statistics III.** See PM 4410.

**4520. Experimental Design II.** Selected topics in ANOVA and ANCOVA including factorial experiments and unbalanced
designs.

Prerequisite: ST 3520.

**4530. Survey Sampling II.** 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: M 2000 and ST 3530.

**4540. Time Series II.** 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.

Prerequisite: PM/ST 3411 and ST 3540.

**4550. Non-parametric Statistics.** 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 ST3520 or ST3521, or PM/ST3411.

**4560. Continuous Multivariate Analysis.** The multivariate normal distribution and its marginal and conditional
distributions, properties of the Wishart distribution, Hotelling's T^{2} statistic, a selection of techniques chosen from among
MANOVA, multivariate regression, principal components, factor analysis, discrimination and classification, clustering.

Prerequisite: M2051, PM/ST3410 and one of ST3520, or ST/PM3411, or ST3521.

**4561. Discrete Multivariate Analysis.** 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: ST 3520 or ST 3521.

**4585. Computational Statistics.** 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: M2000, ST 3520, ST 3521. AM/PM 2130 is recommended.

**4590. Statistical Analysis of Data I (F).** 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 ST3520, or ST3521, or PM/ST3411.

**4599. Honours Comprehensive with Directed Readings.** 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.

Last modified on May 21, 2002 by MaryJane Puxley