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Duggal, Krishan L.; B.A. (Panjab), M.A. (Agra), M.Sc., Ph.D. (Windsor)—1968.
Tracy, Derrick Shannon; B.Sc., M.Sc. (Lucknow), M.S., Sc.D. (Michigan)—1965.
McDonald, James F.; B.S., Ph.D. (Wayne State)—1967.
Chandna, Om Parkash; B.A. (Panjab), M.A. (Delhi), M.Sc., Ph.D. (Windsor)—1968.
Kaloni, Purna N.; M.Sc. (Allahabad), M. Tech., Ph.D. (Indian Inst. of Tech.)—1970.
Lemire, Francis William; B.Sc. (Windsor), M.Sc., Ph.D. (Queen's)—1970.
Wigley, Neil M.; B.A., Ph.D. (California)—1970.
Britten, Daniel J.; B.A. (Merrimack College), M.S., Ph.D. (Iowa)—1971.
Wong, Chi Song; B.S. (National Taiwan U.), M.S. (Oregon), M.S., Ph.D. (Illinois-Urbana)—1971.
Barron, Ronald Michael; B.A., M.Sc. (Windsor), M.S. (Stanford), Ph.D. (Carleton)—1975.
Fung, Karen Yuen; B.A., M.S., Ph.D. (UCLA)—1976.
Paul, Sudhir R.; B.Sc., M.Sc. (Dacca), Ph.D. (Wales)—1982.
Caron, Richard J.; B.M., M.M., Ph.D. (Waterloo)—1983. (Head of the Department)
Zamani, Nader G.; B.Sc. (Case Western), M.Sc., Ph.D. (Brown)—1986.
Atkinson, Harold R.; B.A. (Western Ontario), M.Sc. (Assumption), Ph.D. (Queen's)—1964.
Manley, Paul L.; B.Sc., M.Sc. (Alberta)—1967.
Gold, Alan John; B.A. (Windsor),Dip. D'Etudes, Doct. de Spec. (Clermont)—1969.
McPhail, Gerard; B.Sc., M.Sc. (Queen's), Ph.D. (Toronto)—1969.
Selby, Michael Allen; B.Sc. (Manitoba), M.A., Ph.D. (Cornell), A.S.A.—1970.
Traynor, Tim Eden; B.A., M.A. (Saskatchewan), Ph.D. (British Columbia)—1971.
Hlynka, Myron; B.Sc. (Manitoba), M.A., Ph.D. (Pennsylvania State)—1986.
Hu, Zhiguo; B.Sc., M.Sc. (Northeast), Ph.D. (Alberta)—1993.
Students are reminded that, as indicated in the course descriptions, certain Mathematics and Statistics courses may not be available for credit in some or all of the degree programs outlined below.
Mathematics majors must obtain a grade of C- or better in each Mathematics or Statistics course which is explicitly required in their program of registration. Students registered in the combined Honours Mathematics and Computer Science program also must obtain a grade of at least C- in all required Computer Science courses.
The general Bachelor of Arts (Mathematics) program is subject to the regulations of the Faculty of Science, except that the requirement for a minimum of twenty courses in the Faculty of Science is waived.
Total courses: thirty.
Major requirements: twelve courses, including 62-100, 62-110, 62-111, 62-120, 62-210 (or 62-215), 62-211 (or 62-216), 62-218, and 65-250 (or 65-253); plus four other courses at the 200 level or above.
(a)
four courses from the Faculties of Arts and Social Science, with at least one from each;
(b)
four courses from any department, school, or faculty, including Mathematics and Statistics;
(c)
ten courses from any department, school, or faculty, excluding Mathematics and Statistics.
The general Bachelor of Science (Mathematics) program is subject to the regulations of the Faculty of Science (see 5.3.1).
Total courses: thirty.
Major requirements: twelve courses, including 62-100, 62-110, 62-111, 62-120, 62-210 (or 62-215), 62-211 (or 62-216), 62-218, and 65-250 (or 65-253); plus four other courses at the 200 level or above.
(a)
60-104 and 60-206;
(b)
four of 55-104, 55-105, 59-110, 59-135, 61-100, 61-101, 64-110, or 64-111;
(c)
two additional courses from the Faculty of Science, excluding Mathematics and Statistics;
(d)
four courses from the Faculties of Arts and Social Science, with at least one from each;
(e)
four additional courses from any department, school, or faculty, including Mathematics and Statistics;
(f)
two courses from any department, school, or faculty excluding Mathematics and Statistics.
The Bachelor of Arts (Honours Mathematics) program is subject to the regulations of the Faculty of Science (see 5.3.2).
Total courses: forty.
Major requirements: twenty-five courses, consisting of 62-100, 62-110, 62-111, 62-120, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, 62-321, 65-250, and 65-251; plus three other courses at the 200 level or above; and four other courses at the 300 level or above; plus at least four courses at the 400 level.
Other requirements: 60-104; and fourteen courses from any department, school, or faculty.
The Bachelor of Science (Honours Mathematics) program is subject to the regulations of the Faculty of Science (see 5.3.2).
Total courses: forty.
Major requirements: twenty-five courses, consisting of 62-100, 62-110, 62-111, 62-120, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, 62-321, 65-250, and 65-251; plus three other courses at the 200 level or above; and four more courses at the 300 level or above; plus at least four courses at the 400 level.
Other requirements:
(a)
60-104 and 60-206;
(b)
four of 55-104, 55-105, 59-110, 59-135, 61-100, 61-101, 64-110, or 64-111;
(c)
two additional courses from the Faculty of Science, excluding Mathematics and Statistics;
(d)
seven courses from any department, school, or faculty, including Mathematics and Statistics.
Pure Mathematics: 60-231, 62-222, 62-332, 62-361, 62-410, 62-411, 62-420, 62-421, 62-422, 65-442, and 65-444.
Statistics: 60-231, 65-340, 65-350, 65-351, 62-410, 65-442, 65-444, 65-450, and 65-451.
Applied Mathematics: 60-231, 62-313, 62-332, 62-360, 62-361, 62-374, 62-380, 62-460, 62-461, 62-470, 62-471, 62-472, 62-480, 62-481, 64-110, 64-111, 64-151, 64-220, 64-221, 64-250, 64-321, 64-322, 64-350, 64-351, 64-420, 64-421, 64-450, 64-451, and 65-376.
Actuarial: 62-292, 62-374, 62-380, 62-480, 62-481, 62-490, 62-492, 65-350, 65-351, 65-376, 65-452, 65-454, 70-151, 70-152, 71-140, 72-171, 72-271, 72-374, 72-376, and 72-377.
The Bachelor of Arts (Honours Mathematics and Statistics) program is subject to the regulations of the Faculty of Science (see 5.3.2).
Total courses: forty.
Major requirements: twenty-seven courses, including:
(a)
sixteen Mathematics (62-) courses, consisting of 62-100, 62-110, 62-111, 62-120, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, and 62-321; plus two other courses at the 200 level or above; and at least two courses at the 400 level;
(b)
seven Statistics (65-) courses, consisting of 65-250, 65-251, 65-350, and 65-351; plus one other course at the 300 level or above; and at least two courses at the 400 level;
(c)
and four additional Mathematics or Statistics courses at the 300 level or above. (Recommended: 62-292, 62-490, 62-492, 65-340, 65-359, 65-442, 65-444, 65-450, 65-451, 65-452, 65-454, and 65-456.)
Other requirements: 60-104; and twelve courses from any department, school, or faculty.
The Bachelor of Science (Honours Mathematics and Statistics) program is subject to the regulations of the Faculty of Science (see 5.3.2).
Total courses: forty.
Major requirements: twenty-seven courses, including:
(a)
sixteen Mathematics (62-) courses, consisting of 62-100, 62-110, 62-111, 62-120, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, and 62-321; plus two other courses at the 200 level or above; and at least two courses at the 400 level;
(b)
seven Statistics (65-) courses, consisting of 65-250, 65-251, 65-350, and 65-351; plus one other course at the 300 level or above; and at least two courses at the 400 level;
(c)
and four additional Mathematics or Statistics courses at the 300 level or above. (Recommended: 62-292, 62-490, 62-492, 65-340, 65-359, 65-442, 65-444, 65-450, 65-451, 65-452, 65-454, and 65-456.)
(a)
60-104 and 60-206;
(b)
four of 55-104, 55-105, 59-110, 59-135, 61-100, 61-101, 64-110, or 64-111;
(c)
two additional courses from the Faculty of Science, excluding Mathematics and Statistics;
(d)
five courses from any department, school, or faculty.
The Bachelor of Science (Honours Mathematics and Computer Science) program is subject to the regulations of the Faculty of Science (see 5.3.2).
Total courses: forty.
Major requirements—Mathematics and Statistics: seventeen courses, consisting of 62-100, 62-110, 62-111, 62-120, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, 62-321, 62-480, 62-481, 65-250, and 65-251; plus one of 62-240 or 65-340.
Major requirements—Computer Science: fourteen courses, consisting of 60-100, 60-102, 60-104, 60-108, 60-212, 60-214, 60-231, 60-254, 60-255, 60-265, and 60-315; plus three additional courses at the 300 level or above.
Additional Major requirements: four further Mathematics, Statistics, or Computer Science courses at the 200 level or above, excluding 60-205 and 60-206. (Recommended: 60-370, 60-372, 60-452, 60-453, 60-454, 62-324, 62-482, 65-350, 65-351, and 65-376.)
Other requirements: five courses from any department, school, or faculty.
For Faculty of Science regulations, see 5.3.2.
Note: Statistics courses not prefixed 65- will not be counted for credit towards any combined honours degree with Mathematics.
The honours Bachelor of Arts combining Mathematics with a non-Science major will consist of:
Total courses: forty.
Major requirements—Mathematics and Statistics: twenty courses, including 62-100, 62-110, 62-111, 62-120, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, 62-321, 65-250, and 65-251; plus two additional courses at the 200 level or above; and two more courses at the 300 level or above; and at least two courses at the 400 level.
Major requirements—Other Subject: as prescribed by that department, school, or faculty.
(a)
60-104;
(b)
any additional, non-major requirements as determined by the second department, school, or faculty;
(c)
additional courses, if necessary, from any department, school, or faculty, to a total of forty courses.
The honours Bachelor of Science combining Mathematics with a Science major other than Computer Science will consist of:
Total courses: forty.
Major requirements—Mathematics and Statistics: twenty courses, including 62-100, 62-110, 62-111, 62-120, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, 62-321, 65-250, and 65-251; plus two additional courses at the 200 level or above; and two more courses at the 300 level or above; and at least two courses at the 400 level.
Major requirements—Other Subject: as prescribed by that department, school, or faculty.
(a)
60-104 and 60-206;
(b)
any additional, non-major requirements as determined by the second department, school, or faculty;
(c)
additional courses, if necessary, from any department, school, or faculty, to a total of forty courses.
See Faculty of Science, 5.3.1.
Bachelor of Science (Science, Technology, and Society)
See Faculty of Science, 5.3.1.
All courses listed will not necessarily be offered each year.
Logic, sets, relations, functions. Development of skills in theoretical mathematics. (Prerequisite: 60-100 or 62-120.) (2 lecture, 2 tutorial hours a week.)
Review of derivatives and their applications. Definite and indefinite integrals. Review of transcendental functions. Applications of the definite integral. (Prerequisites: OAC Algebra and Geometry and OAC Calculus, or equivalents.) (Antirequisites: 62-113, 62-116, and 62-194.) (3 lecture hours, 1 tutorial hour a week.)
Techniques of integration, indeterminate forms and improper integrals, numerical methods and approximation, infinite series, polar coordinates, vector-valued functions. (Prerequisites: 62-110 or 62-116, and 62-120 or 62-126.) (Antirequisites: 62-115 and 62-117.) (3 lecture hours, 1 tutorial hour a week.)
Review of differentiation, exponential, and logarithmic functions. Definite and indefinite integrals. Methods of integration, differential equations, partial derivatives. A variety of applications in life science. (Prerequisite: OAC Calculus, or equivalent.) (Antirequisites: 62-110, 62-116, and 62-194.) (3 lecture hours, 1 tutorial hour a week.)
Differentiation and integration of functions of several variables. Differential equations. Infinite series. Probability. Numerical methods. Applications to life and earth sciences. (Prerequisite: 62-113.) (Antirequisites: 62-111, and 62-117.) (3 lecture hours, 1 tutorial hour a week.)
Review of derivatives and their applications. Definite and indefinite integrals. Review of transcendental functions. Applications of definite integrals. (Prerequisites: OAC Algebra and Geometry and OAC Calculus, or equivalents.) (Antirequisites: 62-110, 62-113, and 62-194.) (3 lecture hours, 1 tutorial hour a week.)
Integration techniques, indeterminate forms and improper integrals, numerical methods and approximation, infinite series, polar coordinates, vector-valued functions. (Prerequisites: 62-110 or 62-116 and 62-120 or 62-126.) (Antirequisites: 62-111 and 62-115.) (3 lecture hours, 1 tutorial hour a week.)
Linear systems, matrix algebra, determinants, vectors in Rn, dot product, orthogonalization, eigenvalues, and diagonalization. (Prerequisite: OAC Algebra and Geometry or equivalent.) (Antirequisites: 62-126 and 62-194.) (3 lecture hours, 1 tutorial hour a week.)
Linear systems, matrix algebra, determinants, vectors in Rn, dot product, orthogonalization, and eigenvalues. (Prerequisite: OAC Algebra and Geometry, or equivalent.) (Antirequisites: 62-120 and 62-194.) (3 lectures hours, 1 tutorial hour a week.)
Systems of linear equations. Simplex method for linear programming. Matrix algebra. Differential calculus, anti-derivatives, definite integrals. Compound interest and annuities. Applications to business and economics. (This course does not meet prerequisite requirements for most other Mathematics and Statistics courses.) (Prerequisite: OAC Calculus.) (Antirequisites: all other 100-level Mathematics courses.) (3 lecture hours, 1 tutorial hour a week.)
Intended for students outside of Mathematics and Science. Selected topics from algebra, analysis, geometry, probability, and statistics. (Not available for credit for students in the Faculty of Science.) (3 lecture hours, 1 tutorial hour a week.)
Review of vector functions of one variable. Differential calculus of functions of more than one variable. Vector differential calculus. Multiple integration. (Prerequisites: 62-111 or 62-117, and 62-120 or 62-126.) (Antirequisite: 62-215.) (3 lecture hours, 1 tutorial hour a week.)
Surface integrals, line integrals, and integral theorems. Ordinary differential equations and the Laplace transform. (Prerequisite: 62-210.) (Antirequisite: 62-216.) (3 lecture hours, 1 tutorial hour a week.)
Real numbers. Limits, sequences, and continuity. Differentiation. (Prerequisites: 62-100, 62-111, and 62-120.) (3 lecture hours, 1 tutorial hour a week.)
Sequences and series of functions. Uniform and absolute convergence. Power Series. Integration. (Prerequisite: 62-212.) (3 lecture hours, 1 tutorial hour a week.)
Quadric surfaces. Vector differential calculus. Multiple integration. Line and surface integrals. (Prerequisites: 62-111 or 62-117, and 62-120 or 62-126.) (Antirequisite: 62-210.) (3 lecture hours, 1 tutorial hour a week.)
Differential equations and Laplace transforms. Series solution of differential equations. Applications to science and engineering. (Prerequisites: 62-111, or 62-117, and 62-120 or 62-126.) (Antirequisite: 62-211.) (3 lecture hours, 1 tutorial hour a week.)
Complex numbers. Analytic functions. Contour integration. Series, Laurent expansions, residues. Application to real integrals. (Credit not allowed towards any honours program in Mathematics.) (Prerequisite: 62-211 or one of 62-215, 62-216; corequisite: the other of 62-215, 62-216.) (3 lecture hours, 1 tutorial hour a week.)
Rigourous study of the following topics: linear systems, vector spaces, linear transformations, projections, pseudo-inverses, determinants, inner product spaces and applications. (Prerequisites: 62-100 and 62-120 .) (3 lecture hours, 1 tutorial hour a week.)
A rigourous treatment of eigenvalues and eigenvectors, diagonalization, similarity problem and canonical form for real and complex matrices; positive definite matrices; computational methods for approximating solutions to systems of linear equations and eigenvalues. (Prerequisite: 62-220.) (3 lecture hours, 1 tutorial hour a week.)
Divisibility, congruences, numerical functions. Theorems of Euler, Fermat, and Wilson. Theory of primes and quadratic residues. (Prerequisites: 62-100 and 62-120.) (3 lecture hours a week.)
Finite combinatorics; counting problems involving set operations, relations and functions; principle of inclusion and exclusion; ordinary and exponential generating functions; recurrence relations. (Prerequisites: 62-100 and 62-111.) (3 lecture hours a week.)
Measurement of interest, elementary and general annuities, amortization schedules and sinking funds, bonds, depreciation, depletion, and capitalized cost. This course helps prepare students for the Society of Actuaries examinations. (Prerequisite: 62-111 or 62-115 or 62-117 or consent of instructor.) (3 lecture hours a week.)
Metric spaces. Countability, compactness, and connectedness. Differentiation of functions of several variables. Implicit and inverse function theorems. (Prerequisite: 62-213.) (3 lecture hours a week.)
Analytic functions. Power series. Elementary functions. Contour integration. Cauchy theorem. Singularities. Residues. Laurent expansions. (Prerequisites: 62-212 and one of 62-211 or 62-215.) (3 lecture hours a week.)
Applications of residue theorem, conformal mapping, and analytic continuation. Poisson kernel, harmonic functions, and asymptotic expansions. (Prerequisite: 62-312 or consent of instructor.) (3 lecture hours a week.)
Introduction to groups, rings, and fields. (Prerequisite: 62-220 or 62-222.) (3 lecture hours a week.)
Coding theory in cryptography and informatics; combinatorial designs and finite geometrics. (Prerequisite: 62-222; 62-321 is recommended.) (3 lecture hours a week.)
Homogeneous coordinates and point transformations. Curves, surfaces, and regions. Intersection, curve/surface fitting, and surface patches. Application to computer graphics, computer-aided geometric/cartographic design, pattern recognition, and image processing. (Prerequisites: 62-120 and 62-210 or 62-215.)
Tensor algebra. Covariant differentiation. Tensor form of gradient, divergence, and curl. Riemann-Christoffel symbols. Curvature tensor. Applications. (Prerequisites: 62-210 and 62-211, or 62-215 and 62-216.) (3 lecture hours a week.)
Regular curves. Curvature, torsion, and Frenet equations. Surfaces, tangent planes, and normal vectors. Distance element. Classification of elliptic, hyperbolic, parabolic, and Euclidean surfaces. (Prerequisite: 62-210 or 62-215.) (3 lecture hours a week.)
Uniform convergence, Fourier Series, Orthonormal bases, Sturm-Liouville eigenvalue problems, eigenfunction expansions, Gamma function, Bessel functions, Legendre polynomials and functions, and the hypergeometric functions. (Prerequisite: 62-211, or 62-215 and 62-216.) (3 lecture hours a week.)
Integrable types of nonlinear equations. Methods of solution. Phase plane and stability analysis. Limit cycles. Nonlinear oscillation and perturbation theories. Existence/uniqueness and comparison/oscillation theorems. (Prerequisite: 62-211 or 62-216.) (3 lecture hours a week.)
Cartesian tensors and analysis. Continuum. Kinematics. Equations of motion. Applications to fluids and solids. (Prerequisites: 62-210 and 62-211, or 62-215 and 62-216.) (3 lecture hours a week.)
Topics covered are: geometric linear programming, the Simplex method, the revised Simplex method, duality theory, sensitivity analysis, project planning and integer programming. Optional topics include: the transportation problem, the upper bounding technique, the dual Simplex method, parametric linear programming, game theory, and goal planning. Completion of some assignments will require the use of computer software packages. This course is intended to help students prepare for some parts of the Society of Actuaries examination on Operations Research (Course 130). Interested students should also take 65-376. (Prerequisite: 62-220 or consent of instructor.) (Antirequisite: 91-312.) (3 lecture hours a week.)
Topics covered are: nonlinear equations in one variable, interpolation, numerical integration (quadrature), and linear systems (direct methods). Optional topics are: numerical differentiation, iterative methods for boundary value problems. Completion of some assignments will require the use of computer software packages. This course is intended to help students prepare for some parts of the Society of Actuaries examination on Numerical Methods (Course 135). (Prerequisites: 62-210 or 62-215, 62-211 or 62-216. 62-120 or 62-126.) (May not be taken for credit after 62-481.) (3 lecture hours a week.)
Propositional logic. Proof theory and model theory of first-order logic. Undecidability. (Prerequisite: 62-213 or 62-221.) (3 lecture hours a week.)
Zermelo-Fraenkel axioms. Ordinal and cardinal numbers. Founding mathematics on set theory. Selected topics. (Prerequisite: 62-213 or 62-221.) (3 lecture hours a week.)
Lebesgue measure and Lebesgue integral. Differentiation and integration. Radon-Nikodym theorem. (Prerequisite: 62-213.) (3 lecture hours a week.)
Metric spaces. Topological spaces. Stone-Weierstrass and Ascoli theorems. Classical Banach spaces. (Prerequisite: 62-410.) (3 lecture hours a week.)
Abstract groups, subgroups, isomorphism theorems, orbits, class equation, quotient groups, Sylow's theorems, metric vector spaces, quadratic forms, basic concepts of orthogonal geometry, the classical groups. (Prerequisites: 62-221 and 62-321.) (3 lecture hours a week.)
Matrix rings, polynomial rings, fields of fractions, principal ideal domains and Euclidean domains, finitely generated modules over a p.i.d. (Prerequisites: 62-221 and 62-321.) (3 lecture hours a week.)
Polynomial rings, splitting fields, The Fundamental Theorem of Galois Theory, Galois' criterion for solvability by radicals, algebraically closed fields, finite fields. (Prerequisites: 62-221 and 62-321.) (3 lecture hours a week.)
Topological spaces. Neighbourhood systems. Homomorphisms. Product and quotient spaces. Separation axioms. Compactness, connectedness. Metric spaces: convergence, completeness, category. (Prerequisite: 62-213.) (3 lecture hours a week.)
General basic concepts for linear partial differential equations. Classification of second-order equations and canonical forms. An introduction to theory of distribution. Sturm-Liouville theory for ODEs. Fourier series and integral transforms with applications to PDEs. (Prerequisites: 62-218 or 62-312, and 62-360.) (3 lecture hours a week.)
Qualitative and quantitative analysis of hyperbolic, parabolic, and elliptic partial differential equations. (Prerequisite: 62-460.) (3 lecture hours a week.)
Kinematics, stress hypothesis, constitutive equations, equations of motion. Ideal fluid flow in two and three dimensions. Introduction to potential theory and use of complex variable theory. Effects of viscosity and compressibility. Introduction to computational problems in two-dimensions. (Prerequisites: 62-210 and 62-211, or 62-215 and 62-216, and 62-218 or 62-312.)
Navier-Stokes equations for viscous incompressible flows, exact solutions, boundary layer theory, and asymptotic methods. Compressible inviscid flows, one-dimensional unsteady flows, two-dimensional irrotational flows, method of characteristics. Introduction to shock waves. (Prerequisite: 62-470.) (3 lecture hours a week.)
Theory of mechanics of solid continuum, including elasticity, plasticity, and viscoelasticity. (Prerequisites: 62-210 and 62-211 or 62-215 and 62-216, and 62-218 or 62-312.) (3 lecture hours a week.)
Topics include: floating point arithmetic, matrix factorizations, condition number of matrices, iterative methods, eigenproblems, singular value decomposition. Completion of some assignments will require computer programming and/or the use of major software packages. (Prerequisites: 62-221 and 60-206.) (3 lecture hours a week.)
Topics include: floating point arithmetic, solution of nonlinear algebraic equations, polynomial and spline interpolation, functional approximation, numerical differentiation and integration, numerical solution of ordinary differential equations, unconstrained minimization. Completion of some assignments will require computer programming and/or the use of major software packages. (Prerequisites: 62-211 and 62-480.) (3 lecture hours a week.)
Topics include: unconstrained optimization, convexity, least squares problems, optimality conditions, penalty methods. Completion of some assignments will require the use of computer software packages. (Prerequisites: 62-210, 62-212, 62-221, and one of 62-374, 62-380, or 65-376.) (3 lecture hours a week.)
Life contingencies. Survival distributions and life tables, life insurance, life annuities, net premiums, net premium reserves. This course helps prepare students for the Society of Actuaries examinations. (Prerequisites: 62-292, 65-251, 62-215, and 62-216 or consent of instructor.) (3 lecture hours a week.)
Selection of topics from: advanced life contingencies, risk theory, survival models, construction and graduation of mortality tables. This course helps prepare students for the Society of Actuaries examinations. (Prerequisite: 62-490 or consent of instructor.) (3 lecture hours a week.)
Advanced topics not covered in other courses. (May be repeated for credit when the topic is different.) (Prerequisite: consent of the instructor.) (3 lecture hours a week.)
Undergraduate Statistics courses taught outside of the Department of Mathematics and Statistics may not be taken for credit in any program in the Department.
Descriptive measures, combinatorics, probability, random variables, special discrete and continuous distributions, sampling distribution, point and interval estimation. (Prerequisite: 62-111.) (Antirequisite: 65-253.) (3 lecture hours, 1 tutorial hour a week.)
Distributions, point and interval estimation, hypothesis testing, contingency tables, analysis of variance, bivariate distributions, regression and correlation, non-parametric methods. (Prerequisite: 65-250.) (Antirequisite: 65-253.) (3 lecture hours, 1 tutorial hour a week.)
Descriptive statistics. Probability, discrete and continuous distributions. Point and interval estimation. Hypothesis testing. Goodness-of-fit. Contingency tables. (Prerequisite: Grade 12 Advanced Level Mathematics or OAC Finite Mathematics.) (Antirequisite: 65-250.) (3 lecture hours, 1 tutorial hour a week.)
Conditional probabilities and expectations. Markov chains. Poisson processes, renewal theory, reliability, queueing theory. (Prerequisites: 65-251, and either 62-210 and 62-211, or 62-215 and 62-216.) (3 lecture hours a week.)
Axioms of theory of probability. Discrete and continuous distributions including binomial, Poisson, exponential, normal chi-square, gamma, t, and F distributions. Multivariate distributions, conditional distributions, independence, expectation, moment generating functions, charateristic functions, transformation of random variables, order statistics, law of large numbers, central limit theorem. (Prerequisite: 65-251.) (3 lecture hours a week.)
Point and interval estimations, properties of estimators, methods of estimation, least squares estimation and linear models, Bayesian estimation, Rao-Blackwell theorem, tests of hypotheses, Neyman-Pearson Lemma, analysis of variance. (Prerequisite: 65-350.) (3 lecture hours a week.)
Selected topics in statistics. The course may vary from year to year. (Prerequisite: consent of instructor.) (3 lecture hours a week.)
Topics covered are: deterministic and stochastic dynamic programming, queuing theory, decision analysis, and simulation. Optional topics include: inventory theory, forecasting, and Markov processes. Completion of some assignments will require the use of computer software packages. This course is intended to help students prepare for some parts of the Society of Actuaries examination on Operations Research (Course 130). Interested students should also take 62-374. (Prerequisite: 65-250 or 65-253.) (Antirequisite: 92-412.) (3 lecture hours a week.)
Random variables, expectation, independence, zero-one law, convergence of random variables, laws of large numbers, central limit theorem. (Prerequisite: 62-213 or consent of instructor.) (3 lecture hours a week.)
Conditioning, introduction to stochastic processes, discrete and continuous time Markov Chains. (Prerequisite: 65-442.) (3 lecture hours a week.)
Random vectors and their distributions. Multi-variate normal distribution. Regression and correlation in n variables. Sample moments and their functions. Sampling distributions—exact and asymptotic. Selected topics from: distributions of quadratic forms, order statistics, exponential families. (Prerequisite: 65-351.) (3 lecture hours a week.)
Theory of estimation. Testing of hypotheses. Optimal tests. Estimation and tests in linear models. Selected topics from sequential procedures, nonparametric models, decision theory, Bayesian inference. (Prerequisite: 65-351.) (3 lecture hours a week.)
ANOVA models without and with interactions; randomized block, Latin square, factorial, confounded factorial, balanced incomplete block, and other designs; response surface methodology. (Prerequisite: 65-251 or 65-350.) (3 lecture hours a week.)
Experimental designs and analysis, concepts of blocking, randomization, replication and nesting, multiple linear regression, analysis of covariance, nonparametric procedures, data processing, and use of packaged computer programs. (Prerequisite: 65-250, 65-253 or equivalent; computer experience is desirable.) (Credit will not be allowed toward an Honours Mathematics and Statistics degree.) (This course is regarded as a 300-level course for students in Honours Mathematics or Honours Mathematics and Computer Science.) (3 lecture hours, 1 tutorial hour a week.)
Basic concepts. Simple random and stratified sampling. Ratio and regression methods. Systematic and cluster sampling. Multi-stage sampling, PPS sampling. Errors in surveys. Sampling methods in social investigation. (Prerequisite: 65-251 or 65-350.) (3 lecture hours a week.)
Advanced topics in probability or statistics not covered in other courses. (May be repeated for credit when the topic is different.) (Prerequisite: consent of the instructor.) (3 lecture hours a week.)
An applied course covering multiple linear regression, model assumptions, inference about regression parameters, residual analysis, polynomial regression, multicollinearity, transformations. Topics to be selected from stepwise regression, weighted least squares, indicator variables, nonlinear regression. (Prerequisites: 62-120 and 65-251.) (3 lecture hours a week.)