Office of the Registrar
Faculty of Science (2006/2007)
5.8 Mathematics and Statistics
5.8.1 Programs in Mathematics and Statistics

From the point of view of degree regulations, Applied Mathematics, Pure Mathematics, and Statistics are considered to be one subject area.

The following undergraduate programs are available in the Department:

  1. Major in Applied Mathematics (B.Sc. only)

  2. Major in Pure Mathematics

  3. Major in Statistics

  4. Honours in Applied Mathematics (B.Sc. only)

  5. Honours in Pure Mathematics

  6. Honours in Statistics

  7. Minor in Mathematics

  8. Minor in Statistics

  9. Pure Mathematics/Statistics Joint Honours

  10. Applied Mathematics/Computer Science Joint Major (B.Sc. only)

  11. Applied Mathematics/Economics Joint Major (B.Sc. only)

  12. Applied Mathematics/Physics Joint Major (B.Sc. only)

  13. Pure Mathematics/Computer Science Joint Major (B.Sc. only)

  14. Pure Mathematics/Economics Joint Major (B.Sc. only)

  15. Statistics/Computer Science Joint Major (B.Sc. only)

  16. Statistics/Economics Joint Major (B.Sc. only)

  17. Joint Major in Statistics and Economics (Co-operative) (B.Sc. only)

  18. Applied Mathematics/Chemistry Joint Honours (B.Sc. only)

  19. Applied Mathematics/Physics Joint Honours (B.Sc. only)

  20. Pure Mathematics/Computer Science Joint Honours (B.Sc. only)

  21. Statistics/Computer Science Joint Honours (B.Sc. only)

  22. Statistics/Biology Joint Honours (B.Sc. only)

Details of these programs are given after the Regulations for the Honours Degree of Bachelor of Science.

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

  2. At most 6 credit hours in courses below the 2000 level can be used toward the course requirements in Mathematics and Statistics for the Major, Joint Major, Honours or Joint Honours in Applied Mathematics, Pure Mathematics or Statistics.

  3. In the program descriptions that follow, Mathematics 1000 may be replaced by the former Mathematics 1081.

  4. Credit may be obtained for only one of Statistics 2500, 2510, 2550 and Psychology 2900. Credit may be obtained for only one of Statistics 2501, 2560 (former 2511), and Psychology 2901.

  5. Students with credits in Mathematics or Statistics not listed in this Calendar must consult the department for equivalency before taking any course listed below.

  6. The former Mathematics 1150 and Mathematics 1151 were courses designed specifically for students who intended to graduate with a degree in Primary or Elementary Education. No other students can receive credit for these courses. These courses are not acceptable as alternatives to any other First Year Mathematics course listed in this calendar. Students who have received credit for Education 125 or Mathematics 115/125 cannot receive additional credit for the former Mathematics 1150 or Mathematics 1151 or the current Mathematics 1050 or Mathematics 1051.

    1. For the current academic year the Mathematics Placement Test (MPT) will be used to determine placement in the following courses: Mathematics 1000, Mathematics 1050, Mathematics 1051 and Mathematics 1090.

    2. For subsequent years, students intending to register for the first time in any course below the 2000 level, must first submit a score for one of the following:

      1. Advanced Placement Calculus Examination;

      2. Other standardized tests acceptable to the Department of Mathematics and Statistics.

5.8.3 Faculty Advisors

Each student registered in any program listed above (except for a Minor) will be assigned a Faculty Advisor. Each student's program must be planned with the advice of the Faculty Advisor before presentation to the Head of the Department or his delegate, for approval.

Note:

The Department of Mathematics and Statistics will endeavour to give appropriate advice to students registered in its programs. However, the department points out that it is the responsibility of the student to see that his or her academic program meets the University's regulations in all respects. Students are referred to the UNIVERSITY REGULATIONS - General Academic Regulations (Undergraduate), Registration, Student Responsibility. The department accepts no responsibility for any matter arising from an inappropriate and/or improperly recorded registration.

5.8.4 Course Numbering System

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
  • 1- Applied Mathematics
  • 2- Applied Mathematics and Pure Mathematics
  • 3- Pure Mathematics
  • 4- Pure Mathematics and Statistics
  • 5- Statistics
5.8.5 Major in Applied Mathematics (B.Sc. Only)

Students shall complete the following requirements:

  1. Mathematics 1000, 1001, 2000, 2050, 2051, 3000, 3001, Applied Mathematics 3100, 3132, 3161, Applied Mathematics/Pure Mathematics 3202, 3260, Applied Mathematics 4160, 4190.

  2. Three credit hours in Applied Mathematics courses numbered 3000 or higher.

  3. A computing course, early in your program. Applied Mathematics 2120 is highly recommended.

  4. A designated technical writing course offered by a Science department. Applied Mathematics 2130 is recommended. The technical writing course is prerequisite to some 3000-level courses.

  5. Physics 1050 (or 1020) and 1051.

  6. A statistics course. Statistics 3410 is recommended.

5.8.6 Major in Pure Mathematics

Students shall complete the following requirements:

  1. Mathematics 1000, 1001, 2000, 2050, 2051, Pure Mathematics 2320, Mathematics 3000, Mathematics 3001, Pure Mathematics 3320;

  2. One of Applied Mathematics/Pure Mathematics 3202, 3210, 3260;

  3. One of Pure Mathematics 3330, 3370;

  4. Twelve further credit hours in Pure Mathematics courses numbered 3000 or higher, at least 6 credit hours of which must be in courses numbered 4000 or higher;

  5. A computing course. Applied Mathematics 2120 is recommended.

  6. A designated technical writing course offered by a Science department. Applied Mathematics 2130 is recommended.

  7. A statistics course. Statistics 3410 is recommended.

5.8.7 Major in Statistics

Students shall complete the following requirements:

  1. Mathematics 1000, 1001, 2000, 2050, 2051, 3000, Pure Mathematics/Statistics 3410, 3411, Statistics 3520, 3521, 3530, 4590;

  2. Nine further credit hours in Statistics courses numbered 3000 or higher at least 3 credit hours of which must be in a course numbered 4000 or higher excluding Statistics 4581;

  3. Computer Science 2602.

  4. Mathematics 3001 is recommended.

5.8.8 Honours in Applied Mathematics (B.Sc. Only)

See General Regulations for Honours Degree. Students shall complete the following:

  1. Mathematics 1000, 1001, 2000, 2050, 2051, 3000, 3001, Applied Mathematics 2130, 3100, 3111, 3132, 3161, Applied Mathematics/Pure Mathematics 3202, 3210, 3260, Pure Mathematics/Statistics 3410, Applied Mathematics 4160, 4162, 4170, 4180, 4190, 4199;

  2. A computing course early in the program is required. Applied Mathematics 2120 is recommended.

  3. Physics 1050 (or 1020) and 1051, Physics 3220, and Physics 3230.

  4. nine further credit hours in courses to be chosen from the following: Applied Mathematics/Pure Mathematics 3240, Pure Mathematics/Statistics 3411, Applied Mathematics 4100, Applied Mathematics 4102, Applied Mathematics 4131, Applied Mathematics 4132, Applied Mathematics 4133, Applied Mathematics 4140, Applied Mathematics 4161, Applied Mathematics/Pure Mathematics 4230, Applied Mathematics/Pure Mathematics 4240, Applied Mathematics/Pure Mathematics 4280-4290.

5.8.9 Honours in Pure Mathematics

See General Regulations for Honours Degree. Students shall complete the following requirements:

  1. Mathematics 1000, 1001, 2000, 2050, 2051, 3000, 3001, Applied Mathematics 2130, Pure Mathematics 2320, Statistics 2510, Applied Mathematics/Pure Mathematics 3202, 3210, 3260, Pure Mathematics 3300, 3301, 3320, 3330, 4300, 4310, 4399;

  2. Either Pure Mathematics 3340 or 3370;

  3. Either Pure Mathematics 4320 or 4321;

  4. Twelve further credit hours in Pure Mathematics courses numbered 3000 or higher, at least 9 credit hours of which must be in courses numbered 4000 or higher;

  5. A computing course early in the program is required. Applied Mathematics 2120 is recommended.

5.8.10 Honours in Statistics

See General Regulations for Honours Degree. Students shall complete the following requirements:

  1. Mathematics 1000, 1001, 2000, 2050, 2051, 3000, 3001, Applied Mathematics/Pure Mathematics 3202, 3210, Pure Mathematics/Statistics 3410, 3411, Statistics 3520, 3521, 3530, Pure Mathematics/Statistics 4410, Statistics 4590, 4599;

  2. Eighteen further credit hours in Statistics courses including at least 12 credit hours in courses numbered 4000 or higher excluding Statistics 4581;

  3. Computer Science 2602, Computer Science 3731.

  4. Pure Mathematics/Statistics 4400 and Pure Mathematics/Statistics 4401 are recommended.

5.8.11 Minor in Mathematics

A total of 24 credit hours in courses offered by the Department of Mathematics and Statistics is required of which only 6 credit hours shall be in courses at the 1000 level and at least 6 credit hours shall be in courses numbered 3000 or higher.

5.8.12 Minor in Statistics

The courses required for a minor in Statistics are:

  1. Mathematics 1000, 1001; Statistics 2500 or 2510, Statistics 2501 or 2560.

  2. Twelve further credit hours in Statistics courses numbered 3000 or higher excluding Statistics 4581.

It is recommended that Mathematics 2000 and Mathematics 2050 be taken since they are prerequisite to several further Statistics courses.

5.8.13 Course List

In accordance with Senate's Policy Regarding Inactive Courses, the course descriptions for 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.

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.

5.8.13.1 Foundation Courses

102F, 103F and 104F

Mathematics Skills Program

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

5.8.13.2 Common Core Mathematics Courses

1000

Calculus I

(F) & (W)

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

Four hours per week.

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

Note:

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

1001

Calculus II

(F) & (W)

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

Prerequisite: Mathematics 1000 or 1081.

Note:

Credit cannot be obtained for both Mathematics 1001 and either the former Engineering 1411 or the former Engineering 2413.

1031

Mathematical Problem Solving

- inactive course.

1050

Finite Mathematics I

(F) & (W)

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

Four hours per week.

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

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 Mathematics 1050 and the former 1150.

1051

Finite Mathematics II

(F) & (W)

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

Four hours per week.

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

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 Mathematics 1051 and the former 1151.

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.

Four hours per week.

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

Note:

Students will not receive credit for Mathematics 1090 if they have previously received credit or are currently registered for Mathematics 1000, 1001, the former 1080, or the former 1081.

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. In addition to three lectures per week there will be a one and one-half hour problem lab.

Prerequisite: Mathematics 1001.

Note:

Credit cannot be obtained for both Mathematics 2000 and any of the former Engineering 1411, 1412, 2412, or 2413.

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.

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

Note:

Credit cannot be obtained for both Mathematics 2050 and the former Engineering 2402.

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.

Prerequisite: Mathematics 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.

Prerequisite: Mathematics 1001.

2091

Introduction to Actuarial Mathematics

covers life tables, life annuities, life insurance, multi-life theory, stationary population, interest rates as a random variable.

Prerequisites: Mathematics 2090 and one of Statistics 2500, 2510, 2550.

3000

Real Analysis I

(F) & (W)

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

Three lecture hours and one laboratory hour per week.

Prerequisite: Mathematics 2000.

Note:

Credit can be obtained for only one of Mathematics 3000 and the former Mathematics 2001.

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.

Three lecture hours and one laboratory hour per week.

Prerequisite: Mathematics 3000.

Note:

Credit cannot be received for both of Mathematics 3001 and the former Applied Mathematics/Pure Mathematics 3201.

5.8.13.3 Applied Mathematics Courses

2120

Introduction to Mathematical Programming

(F)

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: Mathematics 1000 or 1081.

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 Applied Mathematics 2130, Computer Science 2710 or Computer Science 2602 cannot receive credit for Applied Mathematics 2120.

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.

Prerequisite: Mathematics 1001 and (Applied Mathematics 2120 or Computer Science 2710 or 2602 or permission of the Head of Department).

Notes:

  1. 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.

  2. This course 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.

Three lecture hours per week.

Prerequisites: Applied Mathematics/Pure Mathematics 3260 and a technical writing course offered by a Science department (Applied Mathematics 2130 is recommended).

Note:

Credit can be obtained for only one of Applied Mathematics 3100 and the former 3190.

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.

Prerequisite: Applied Mathematics/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.

Prerequisites: Applied Mathematics 2130 and Applied Mathematics/Pure Mathematics 3260.

Note:

Credit cannot be obtained for both Applied Mathematics 3132 and Computer Science 3731.

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.

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

Prerequisite: Mathematics 2000 and 2050.

Note:

Credit cannot be obtained for both Applied Mathematics/Pure Mathematics 3202 and Physics 3810.

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.

Prerequisite: 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 coloring, planarity, trees, network flows, with emphasis on applications including scheduling problems, tournaments, and facilities design.

Prerequisite: Pure Mathematics 2320.

Note:

Credit cannot be obtained for both Applied Mathematics/Pure Mathematics 3240 and Computer Science 2741.

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.

Prerequisite: Mathematics 2000.

Note:

Credit cannot be obtained for both Applied Mathematics/Pure Mathematics 3260 and Engineering 3411.

4100

Applied Functional Analysis

- inactive course.

4102

Stochastic Methods in Applied Mathematics

- inactive course.

4131

Numerical Linear Algebra

- inactive course.

4132

Introduction to Optimization

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

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

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.

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

Prerequisite: Applied Mathematics 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.

Prerequisite: Applied Mathematics 4160.

4180

Introduction to Fluid Dynamics

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

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

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 analyzed. Students will develop a mathematical model and present it in both oral and report form.

Prerequisites: Applied Mathematics 3100, Applied Mathematics 3161 and Applied Mathematics 4160.

4199

Applied Mathematics Honours Project

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

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

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.

Prerequisite: Applied Mathematics/Pure Mathematics 3202.

4240

Differential and Integral Calculus on Manifolds

- inactive course.

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.

5.8.13.4 Pure Mathematics Courses

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.

Prerequisite: Mathematics 1001 or 2050.

Note:

Credit cannot be obtained for both Pure Mathematics 2320 and Computer Science 2740.

3202

Vector Calculus

(F) & (W)

see Applied Mathematics 3202.

3210

Introduction to Complex Analysis

see Applied Mathematics 3210.

3240

Applied Graph Theory

see Applied Mathematics 3240.

3260

Ordinary Differential Equations I

see Applied Mathematics 3260.

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.

Prerequisite: Mathematics 3000.

3301

Integration and Metric Spaces

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

Prerequisite: Mathematics 3001.

3303

Introductory Geometric Topology

- inactive course.

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.

Prerequisite: Pure Mathematics 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.

Prerequisite: Pure Mathematics 2320 or Mathematics 2051.

3331

Projective Geometry

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

Prerequisite: Pure Mathematics 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.

Prerequisite: Pure Mathematics 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.

Prerequisite: Pure Mathematics 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.

One and a half hour tutorial period weekly.

Prerequisite: 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.

One and a half hour tutorial period weekly.

Prerequisite: Pure Mathematics/Statistics 3410.

4230

Differential Geometry

see Applied Mathematics 4230.

4240

Differential and Integral Calculus on Manifolds

see Applied Mathematics 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

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

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

4301

Algebraic Topology

- inactive course.

4302

Functional Analysis

- 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.

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

Prerequisite: Pure Mathematics 3320.

4321

Group Theory

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

Prerequisite: Pure Mathematics 3320.

4331

Galois Theory

- inactive course.

4340

Combinatorial Analysis

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

Prerequisite: Mathematics 2000 and Pure Mathematics 3340.

4341

Combinatorial Designs

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

Prerequisite: Pure Mathematics 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.

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

4400

Lebesgue Integration

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

Prerequisite: Mathematics 3001.

4401

Probability Theory

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

Prerequisite: Mathematics 3000 and Pure Mathematics/Statistics 3410.

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.

Prerequisite: Mathematics 2051 and Pure Mathematics/Statistics 3411.

5.8.13.5 Statistics Courses

Note:

All 2000 level statistics courses, Statistics 3410, 3411, 4590, and 4591 have a laboratory period weekly.

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.

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

Note:

Credit can be obtained for only one of Statistics 2500, 2510, 2550, and Psychology 2900. Statistical computer package will be use in the laboratory, but no prior computing experience is assumed.

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.

Prerequisite: Statistics 2500 or 2510.

Note:

Credit can be obtained for only one of Statistics 2501, 2560, the former 2511, and Psychology 2901. Statistical computer package will be used in the laboratory.

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.

Prerequisite: Mathematics 1000 or 1081.

Note:

Credit can be obtained for only one of Statistics 2500, 2510, 2550, Psychology 2900, and Engineering 3423. Normally offered twice a year, including the fall.

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.

Prerequisite: Mathematics 1000 or 1081.

Note:

Credit can be obtained for only one of Statistics 2500, 2510, 2550, and Psychology 2900. Statistical computer package will be used in the laboratory, but no prior computing experience is assumed.

2560

Further Statistics for Science Students

(W)

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

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

Note:

Credit can be obtained for only one of Statistics 2501, 2560, the former 2511, and Psychology 2901. Statistical computer packages will be used in the laboratory, but no prior computing experienced is assumed.

3410

Mathematical Statistics I

see Pure Mathematics 3410

3411

Mathematical Statistics II

see Pure Mathematics 3411

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.

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

Note:

Credit cannot be obtained for both Statistics 3520 and Psychology 3900.

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.

Prerequisite: Mathematics 2050 and either Pure Mathematics/Statistics 3411 or both Mathematics 1001 and one of Statistics 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.

Prerequisite: Either Pure Mathematics/Statistics 3411 or both Mathematics 1001 and one of Statistics 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.

Prerequisite: Either Pure Mathematics/Statistics 3411 or both Mathematics 1001 and one of Statistics 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.

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

3590

Statistics in Applied Research

- inactive course.

4400

Lebesgue Integration

see Pure Mathematics 4400

4401

Probability Theory

see Pure Mathematics 4401

4402

Stochastic Processes

see Pure Mathematics 4402

4410

Mathematical Statistics III

see Pure Mathematics 4410

4520

Experimental Design II

(W)

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

Prerequisite: Statistics 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.

Prerequisites: Mathematics 2000 and Statistics 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.

Prerequisite: Pure Mathematics/Statistics 3411 and Statistics 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.

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

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

Prerequisite: Statistics 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.

Prerequisites: Mathematics 2000, Statistics 3520, 3521. Applied Mathematics/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.

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

4591

Statistical Analysis of Data II

- inactive course.

4599

Honours Comprehensive with Directed Readings

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

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