University of Windsor - Academic Calendar, 1998-1999

For further information, see our World Wide Web page:
http://www.cs.uwindsor.ca/units/math

OFFICERS OF INSTRUCTION

Professors Emeriti
Duggal, Krishan L.; B.A. (Panjab), M.A. (Agra), M.Sc., Ph.D. (Windsor)—1968.

Smith, Alexander Cormac; B.Sc., M.Sc., Ph.D. (Dublin)-1963
Tracy, Derrick Shannon; B.Sc., M.Sc. (Lucknow), M.S., Sc.D. (Michigan)—1965.

Wigley, Neil M.; B.A., Ph.D. (California)-1970

Professors
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.

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.

Zamani, Nader G.; B.Sc. (Case Western), M.Sc., Ph.D. (Brown)—1986.

Associate Professors
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.

Assistant Professor
Hu, Zhiguo; B.Sc., M.Sc. (Northeast), Ph.D. (Alberta)—1993.

Adjunct Professor
Fleisher, Isidore; B.Sc. (Brooklyn), M.Sc., Ph.D. (Chicago)—1985.

Cross-Appointments
Brill, Percy; B.Sc. (Carleton), M.A. (Columbia), Ph.D. (Toronto)—1984.

Fan, Yanqin; B.Sc. (Jilin), M.A., Ph.D. (Western Ontario)—1989.
Gencay, Ramazan; B.Sc. (Middle East Tech. U., Ankara), M.A. (Guelph), Ph.D. (Houston)—1991.

4.10.1 PROGRAMS OF STUDY

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.

All programs in Mathematics are subject to the general University and College of Engineering and Science regulations as outlined in the relevant sections of this calendar except that B.A. programs in Mathematics do not require a minimum of twenty science courses for graduation. Additionally, 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.

Bachelor of Arts (Mathematics)
Total courses: thirty.
Major requirements: twelve courses, including 62-100, 62-120, 62-140, 62-141, 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.

Other requirements:
(a) 60-140 and 60-141;
(b) four courses from Arts, Languages or Social Science, with at least one from Arts/Languages and one from Social Science;
(c) four courses from any area of study, including Mathematics and Statistics;
(d) eight courses from any area of study, excluding Mathematics and Statistics.

Bachelor of Science (Mathematics)
Total courses: thirty.
Major requirements: twelve courses, including 62-100, 62-120, 62-140, 62-141, 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.

Other requirements:
(a) 60-140 and 60-141;
(b) two, two course sequences from 55-140 and 55-141, 59-140 and 59-141, or 61-140 and 61-141;
(c) two additional Science courses, excluding Mathematics and Statistics;
(d) four courses from Arts, Languages or Social Science, with at least one from Arts/Languages and one from Social Science;
(e) four additional courses from any area of study, including Mathematics and Statistics;
(f) two courses from any area of study excluding Mathematics and Statistics.

Bachelor of Arts (Honours Mathematics)
Total courses: forty.
Major requirements: twenty-five courses, consisting of 62-100, 62-120, 62-140, 62-141, 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: 60-140 and 60-141; and thirteen courses from any area of study.

Bachelor of Science (Honours Mathematics)
Total courses: forty.
Major requirements: twenty-five courses, consisting of 62-100, 62-120, 62-140, 62-141, 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) 60-140 and 60-141;
(b) two, two course sequences from 55-140 and 55-141, 59-140 and 59-141, 61-140 and 61-141, or 64-140 and 64-141;
(c) two additional Science courses, excluding Mathematics and Statistics;
(d) seven courses from any area of study, including Mathematics and Statistics.

SUGGESTED COURSES
FOR MATHEMATICS SPECIALIZATIONS
Pure Mathematics: 60-231, 62-222, 62-332, 62-361, 62-410, 62-411, 62-420, 62-421, 62-422, 65-442, and 65-443.
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, 64-140, 64-141, 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.

Bachelor of Arts (Honours Mathematics and Statistics)
Total courses: forty.
Major requirements: twenty-seven courses, including:
(a) twelve Mathematics (62-) courses, consisting of 62-100, 62-120, 62-140, 62-141, 62-210, 62-211, 62-212, 62-213, 62-220, 62-221, 62-312, and 62-321;
(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 eight additional Mathematics or Statistics courses at the 200 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: 60-140 and 60-141; and eleven courses from any subject area.

Bachelor of Science (Honours Mathematics and Statistics)
Total courses: forty.
Major requirements: twenty-seven courses, including:
(a) twelve Mathematics (62-) courses, consisting of 62-100, 62-120, 62-140, 62-141, 62-210, 62-211,
62-212, 62-213, 62-220, 62-221, 62-312, and 62-321;
(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 eight additional Mathematics or Statistics courses at the 200 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.)

Bachelor of Science (Honours Mathematics and Computer Science)
Total courses: forty.
Major requirements—Mathematics and Statistics: seventeen courses, consisting of 62-100, 62-120,
62-140, 62-141, 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, 60-104, 60-140,
60-141, 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 area of study.

Other Combined B.A./B.Sc. Honours Programs
Notes:
1) The B.Sc. degree is awarded when combining Mathematics with another Science subject; the B.A.
degree is awarded when combining Mathematics with a subject outside Science.
2) Statistics courses not prefixed 65- will not be counted for credit towards any combined honours degree with Mathematics.
Honours programs combining Mathematics with a second major area of study (other than Computer Science) will consist of:

Total courses: forty.

Major requirements—Mathematics and Statistics: twenty courses, including 62-100, 62-120, 62-140, 62-141, 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 area of study.

Other requirements:
(a) 60-140 and 60-141;
(b) any additional, non-major requirements as determined by the second area of study;
(c) additional courses, if necessary, from any area of study to a total of forty courses.

Minor in Mathematics
A minor in Mathematics consists of at least six courses taken from Mathematics and Statistics, with a minimum average of 5.0, including 62-120, 62-140 and 62-141. The remaining three or more
courses must be chosen among 62-100 and courses in Mathematics and/or Statistics numbered 200 or higher.

Bachelor of Science (General Science)
See College of Engineering and Science, 4.2.1.

Bachelor of Science
(Science, Technology, and Society)
See College of Engineering and Science, 4.2.2

4.10.2 COURSE DESCRIPTIONS— MATHEMATICS

All courses listed will not necessarily be offered each year.

62-100. Mathematical Foundations
Logic, sets, relations, functions. Development of skills in theoretical mathematics. (Prerequisite: 60-100 or 62-120.) (2 lecture, 2 tutorial hours a week.)

62-120. Linear Algebra I
Linear systems, matrix algebra, determinants, vectors in Rn, dot product, orthogonalization, eigenvalues, and diagonalization. (Prerequisite: OAC Algebra and Geometry or equivalent.)
(Antirequisite: 62-126.) (3 lecture hours, 1 tutorial hour a week.)

62-126. Linear Algebra (Engineering)
Linear systems, matrix algebra, determinants, vectors in Rn, dot product, orthogonalization, and eigenvalues. (Prerequisite: OAC Algebra and Geometry, or equivalent.) (Antirequisite: 62-120.) (3
lectures hours, 1 tutorial hour a week.)

62-140. Calculus A
Limits and continuity; differential calculus with applications, extending OAC Calculus; related rates, differentials. Mean Value Theorem. Antiderivatives, Riemann sums and the definite integral.
Fundamental Theorem of Calculus. Selected integration techniques. Selected applications of the definite integral. (Prerequisite: OAC Calculus, or equivalents.) (3 lecture hours, 1 tutorial hour a week.)

62-141. Calculus B
Indeterminate forms and l'Hopital's Rule. Further techniques of integration. Improper integrals, numerical integration. Separable differential equations. Further applications of definite integrals.
Polar and parametric coordinates. Infinite sequences and series: tests for convergence, power series (Taylor, Maclaurin, binomial). (Prerequisite: 62-140) (3 lecture hours, 1 tutorial hour a week.)

62-194. Mathematics for Business
Mathematics of finance. Solutions of linear equations, matrices, linear inequalities, simplex method for linear programming. Probability theory. (This course is intended for students in the Faculty of Business Administration.) (Prerequisite: Any OAC Mathematics course.) (3 lecture hours, 1 tutorial hour a week.)

62-198. Ideas in Mathematics
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 College of Engineering and Science.) (3 lecture hours, 1 tutorial hour a week.)

62-210. Multivariable and Vector Differential Calculus
Review of vector functions of one variable. Differential calculus of functions of more than one variable. Vector differential calculus. Multiple integration. (Prerequisites: 62-141, and 62-120 or
62-126.) (Antirequisite: 62-215.) (3 lecture hours, 1 tutorial hour a week.)

62-211. Vector Integral Calculus and Differential Equations
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.)

62-212. Introduction to Analysis I
Real numbers. Limits, sequences, and continuity. Differentiation. (Prerequisites: 62-100, 62-120, and 62-141.) (3 lecture hours, 1 tutorial hour a week.)

62-213. Introduction to Analysis II
Sequences and series of functions. Uniform and absolute convergence. Power Series. Integration. (Prerequisite: 62-212.) (3 lecture hours, 1 tutorial hour a week.)

62-215. Vector Calculus
Quadric surfaces. Vector differential calculus. Multiple integration. Line and surface integrals. (Prerequisites: 62-141, and 62-120 or 62-126.) (Antirequisite: 62-210.) (3 lecture hours, 1 tutorial hour a week.)

62-216. Differential Equations
Differential equations and Laplace transforms. Series solution of differential equations. Applications to science and engineering. (Prerequisites: 62-141, and 62-120 or 62-126.) (Antirequisite: 62-211.) (3 lecture hours, 1 tutorial hour a week.)

62-218. Complex Variables
Complex numbers. Analytic functions. Contour integration. Series, Laurent expansions, residues. Application to real integrals. (Credit not allowed towards any honours program in Mathematics.) (Prerequisite: 62-210 or 62-215; corequisite: 62-211 or 62-216.) (3 lecture hours, 1 tutorial hour per week.)

62-220. Linear Algebra II
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.)

62-221. Linear Algebra III
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.)

62-222. Number Theory
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.)

62-240. Combinatorics
Finite combinatorics; counting problems involving set operations, elations and functions; principle of inclusion and exclusion; ordinary and exponential generating functions; recurrence relations. (Prerequisites: 62-100 and 62-141.) (3 lecture hours a week.)

62-292. Theory of Interest
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: 62-141 or consent of instructor.) (3 lecture hours a week.)

62-310. Principles of Analysis I
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.)

62-312. Complex Analysis
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.)

62-313. Applied Complex Analysis
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.)

62-321. Abstract Algebra
Introduction to groups, rings, and fields. (Prerequisite: 62-220 or 62-222.) (3 lecture hours a week.)

62-324. Applied Algebra
Coding theory in cryptography and informatics; combinatorial designs and finite geometrics. (Prerequisite: 62-222; 62-321 is recommended.) (3 lecture hours a week.)

62-330. Computational Geometry
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.)

62-332. Tensor Analysis
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.)

62-338. Differential Geometry
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.)

62-360. Special Functions
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.)

62-361. Differential Equations
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.)

62-371. Continuum Mechanics
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.)

62-374. Linear Programming
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.)

62-380. Numerical Methods
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.)

62-400. Mathematical Logic
Propositional logic. Proof theory and model theory of first-order logic. Undecidability. (Prerequisite: 62-213 or 62-221.) (3 lecture hours a week.)

62-401. Axiomatic Set Theory
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.)

62-410. Real Analysis I
Lebesgue measure and Lebesgue integral. Differentiation and integration. Radon-Nikodym theorem. (Prerequisite: 62-213.) (3 lecture hours a week.)

62-411. Real Analysis II
Metric spaces. Topological spaces. Stone-Weierstrass and Ascoli theorems. Classical Banach spaces. (Prerequisite: 62-410.) (3 lecture hours a week.)

62-420. Introduction to Group Theory
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.)

62-421. Introduction to Ring Theory
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.)

62-422. Introduction to Field Theory
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.)

62-434. Point Set Topology
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.)

62-460. Applied Mathematics Methods I
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.)

62-461. Applied Mathematics Methods II
Qualitative and quantitative analysis of hyperbolic, parabolic, and elliptic partial differential equations. (Prerequisite: 62-460.) (3 lecture hours a week.)

62-470. Fluid Dynamics I
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.)

62-471. Fluid Dynamics II
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.)

62-472. Solid Mechanics
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.)

62-480. Numerical Linear Algebra
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 60-141.) (3 lecture hours a week.)

62-481. Numerical Analysis
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.)

62-482. Mathematical Programming
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.)

62-490. Actuarial Mathematics I
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.)

62-492. Actuarial Mathematics II
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.)

62-498. Topics in Mathematics
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.)

4.10.3 COURSE DESCRIPTIONS— STATISTICS

Undergraduate Statistics courses taught outside Mathematics and Statistics may not be taken for credit in any mathematics program.

65-250. Introduction to Probability
Descriptive measures, combinatorics, probability, random variables, special discrete and continuous distributions, sampling distribution, point and interval estimation. (Prerequisite: 62-141.) (Antirequisite: 65-253.) (3 lecture hours, 1 tutorial hour a week.)

65-251. Introduction to Statistics
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.)

65-253. Statistics for the Sciences
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.) (Antirequisites: 02-250, 73-105, 73-205, 85-222, and 65-250.) (3 lecture hours, 1 tutorial hour a week.)

65-340. Applied Probability
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.)

65-350. Probability
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, characteristic functions, transformation of random variables, order statistics, law of large numbers, central limit theorem. (Prerequisite: 65-251.) (3 lecture hours a week.)

65-351. Statistics
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.)

65-359. Topics in Statistics
Selected topics in statistics. The course may vary from year to year. (Prerequisite: consent of instructor.) (3 lecture hours a week.)

65-376. Stochastic Operations Research
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: 91-412.) (3 lecture hours a week.)

65-442. Probability Theory I
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.)

65-443. Probability Theory II
Conditioning, introduction to stochastic processes, discrete and continuous time Markov Chains. (Prerequisite: 65-442.) (3 lecture hours a week.)

65-450. Distribution Theory
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.)

65-451. Statistical Inference
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.)

65-452. Experimental Designs
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.)

65-453. Statistics (Life/Social Sciences)
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.)

65-454. Sampling Theory
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.)

65-455. Topics in Statistics
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.)

65-456. Regression
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.)

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4.10 Mathematics and Statistics