2001-2002
Undergraduate Calendar | 2001-2002
Undergraduate Calendar |
||
| 2001-2002 UNDERGRADUATE CALENDAR: COURSES | ||
| Carleton University |
Mathematics and Statistics Courses
Not all of the following courses are offered in a given year. For an up-to-date statement of course offerings for 2001-2002, please consult the Registration Instructions and Class Schedule booklet published in the summer.
Mathematics 69.007*
Introductory Calculus
Limits and continuity. Differentiation. Trigonometric, logarithmic, and exponential functions and their derivatives; curve sketching; applied problems in maxima and minima, and related rates.
Not available for degree credit for students who have successfully completed an OAC in Calculus/or an equivalent High School Calculus course.
Precludes additional credit for Business 42.173.
Prerequisite: Grade 12 Mathematics (Advanced/Academic Level) or Mathematics 69.006* or equivalent. It is strongly recommended that Mathematics 69.017* or the equivalent be taken before 69.007*.
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Mathematics 69.017*
Algebra and Geometry
Vectors in the plane and in 3-space. Linear combinations and linear independence. Equations of lines and planes in space. Solution of systems of linear equations. Complex numbers (including de Moivre's Theorem, and n-th roots). Proofs by induction.
Not available for degree credit for students who have successfully completed an OAC in Algebra and Geometry/or an equivalent High School Algebra course.
Prerequisite: Grade 12 Mathematics (Advanced/Academic Level) or Mathematics 69.006* or equivalent.
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.Mathematics 69.102
Calculus
This course is strongly recommended for students intending to specialize in mathematics, statistics, physics, or related areas. Limits, differentiation, the definite integral, elementary functions, techniques of integration, parametric equations and polar coordinates. Improper integrals, L'Hôpital's rules, sequences and series, Taylor's formulae, introduction to differential equations.
Precludes additional credit for Mathematics 69.104*, 69.105*, 69.107*, 69.109*, 69.207*, and for 69.201, 69.202.
Prerequisites: (i) a pre-university calculus course with a grade of 65 percent or better; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*, or permission of the School. (See Prerequisites for First-year Calculus and Algebra Courses, this page.)
Lectures three hours a week and one hour tutorial.
Note: Although the main prerequisite for Mathematics 69.102 is a grade of 65 percent or better in a pre-university calculus course, past experience indicates that students with less than 75 percent in their prerequisite calculus have only a small chance of success in Mathematics 69.102.Mathematics 69.104*
Calculus for Engineering Students
The definite and indefinite integral; numerical approximation. Special functions (trigonometric and inverse trigonometric, logarithm and exponential), their derivatives and integrals. Applications: area, volume, average value. Further techniques of integration: integration by parts, partial fractions, and substitutions. Introduction to differential equations.
Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.
Precludes additional credit for Mathematics 69.102, 69.107*, 69.109*.
Prerequisite: an OAC in Calculus, or Mathematics 69.007* (or equivalent).
Lectures three hours a week and one hour tutorial.
Mathematics 69.105*
Differential Equations and Infinite Series for Engineering Students
Further study of first-order differential equations. Linear differential equations with constant coefficients; undetermined coefficients; annihilator operators. Variation of parameters. Euler-Cauchy differential equation. Indeterminate forms. Sequences and series; convergence tests; estimation of sums. Power series; Taylor series; remainders. Use of power series to solve differential equations.
Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.
Precludes additional credit for: Mathematics 69.102, 69.201, 69.202, 69.207*, 69.244*, 70.244* and 70.260.
Prerequisites: (i) Mathematics 69.104*, or a grade of C- or better in 69.107*; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*; or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 69.107*
Elementary Calculus I
Definite and indefinite integrals, differentiation and integration of the elementary functions, techniques and applications of integration.
Precludes additional credit for Mathematics 69.102, 69.104*, 69.109*.
Prerequisite: an OAC in Calculus, or Mathematics 69.007* (or equivalent).
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Notes:
1. Students with less than 60 percent in their pre-university calculus course are advised that past experience indicates their chance of success in Mathematics 69.107* is small.
2. A grade of C- or better in Mathematics 69.107* is a prerequisite for certain 200-level Mathematics courses.
Mathematics 69.109*
Calculus: with Applications to Business and Economics
Definite and indefinite integrals; integration of the elementary functions; some techniques of integration. Functions of several variables; partial differentiation; constrained optimization. Selected applications in business and economics.
Precludes additional credit for Mathematics 69.102, 69.104*, and 69.107*.
Prerequisite: an OAC in Calculus, or Mathematics 69.007* (or equivalent).
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Note: Students with less than 60 percent in their pre-university calculus course are advised that past experience indicates their chance of success in Mathematics 69.109* is small.
Mathematics 69.112
Algebra
Fields, complex numbers, vector algebra and geometry in 2 and 3 dimensions, matrix algebra, linear dependence, bases, linear transformations, bilinear and quadratic forms, inner products, eigenvalues, principal axis theorem. Strongly recommended for students intending to specialize in mathematics, statistics, physics, or related areas.
Precludes additional credit for Mathematics 69.114*, 69.117*, 69.119*, 69.217*.
Prerequisites: (i) a pre-university algebra course with a grade of 65 percent or better, and (ii) an OAC in Calculus, or Mathematics 69.007*, or permission of the School. (See Prerequisites for First-year Calculus and Algebra Courses, p.337)
Lectures three hours a week and one hour tutorial.
Note: Although the main prerequisite for Mathematics 69.112 is a grade of 65 percent or better in a pre-university algebra course, past experience indicates that students with less than 75 percent in their prerequisite mathematics have only a small chance of success in Mathematics 69.112.
Mathematics 69.114*
Linear Algebra for Engineering and Computer Science Students
Systems of linear equations. Matrix algebra. Determinants. Complex numbers. Eigenvalues. Diagonalization and applications.
Restricted to students in the Faculty of Engineering, in the School of Computer Science, or in B.Sc.(Honours) in Applied Physics.
Precludes additional credit for Mathematics 69.112, 69.117*, 69.119*.
Prerequisite: an OAC in Algebra and Geometry, or Mathematics 69.017* (or equivalent).
Lectures three hours a week and one hour tutorial.
Mathematics 69.117*
Linear Algebra I
Systems of linear equations; vector space of n-tuples, subspaces and bases; matrix transformations, kernel, range; matrix algebra and determinants. Inner products and orthogonality. Eigenvalues, diagonalization and applications. Emphasis throughout this course will be on the computational aspects (and not on theoretical aspects).
Precludes additional credit for Mathematics 69.112, 69.114*, 69.119*.
Prerequisite: an OAC in Algebra and Geometry, or Mathematics 69.017* (or equivalent).
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Note: A grade of C- or better in Mathematics 69.117* is a prerequisite for certain 200-level Mathematics courses.
Mathematics 69.119*
Linear Algebra: With Applications to Business and Economics
Algebraic concepts, systems of linear equations, vector algebra; matrix algebra, rank, inversion, determinants; linear programming - geometric approach, simplex method, etc. Applications in the fields of business and economics.
Precludes additional credit for Mathematics 69.112, 69.114*, 69.117*, and for Mathematics 69.132* (Architecture 79.201*).
Prerequisite: An OAC in Algebra and Geometry, or Mathematics 69.017* (or equivalent).
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Mathematics 69.185*
Discrete Structures I
An introduction to discrete mathematics and discrete structures. Topics include: propositional and predicate calculus, Boolean algebra, introduction to complexity of algorithms, mathematical reasoning, counting, recurrences, relations, introduction to graphs. (Also listed as Computer Science 95.185*.)
This course is available to Science students only as a free option.
Prerequisites: Two OACs in Mathematics, and one of Computer Science 95.105* or 95.107* (which may be taken concurrently).
Lectures three hours a week.
Mathematics 69.204*
Multivariable Calculus for Engineering Students
Fourier series; expansions for even and odd functions; half-range expansions. Surfaces in R3. Differential calculus of functions of several variables. Extrema and Lagrange multipliers. Exact differentials. Line integrals. Double integrals; polar coordinates; applications. Triple integrals; cylindrical and spherical coordinates; applications.
Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.
Precludes additional credit for: Mathematics 69.201, 69.202, 69.208*, 69.209* and 70.200.
Prerequisites: (i) Mathematics 69.105* or 69.207*; and (ii) Mathematics 69.114* or 69.117*; or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 69.207*
Elementary Calculus II
Further techniques of integration, improper integrals, polar coordinates, parametric equations, indeterminate forms, sequences and series, Taylor's formula and series, first order and linear differential equations.
Precludes additional credit for Mathematics 69.102, 69.105*, and for 69.201, 69.202.
Prerequisites: (i) Mathematics 69.104*, or a grade of C- or better in Mathematics 69.107* or 69.109*; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*, or permission of the School.
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Mathematics 69.208*
Intermediate Calculus
Partial differentiation, chain rule, gradient, line and multiple integrals with applications, transformations, implicit and inverse function theorems.
Precludes additional credit for Mathematics 69.204*, 69.209*, 70.200, and for 69.201, 69.202.
Prerequisites: Mathematics 69.102 or 69.207*, and 69.112 or 69.117*.
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Mathematics 69.209*
Intermediate Calculus for Science Students
Differential equations; differential calculus of functions of several variables; multiple integration; introduction to Fourier series.
Precludes additional credit for Mathematics 69.201, 69.202, 69.204*, 69.208* and 70.200.
Prerequisites: (i) Mathematics 69.207*, or 69.102; and (ii) Mathematics 69.117* or 69.114* or 69.112; or their equivalents, or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 69.217*
Linear Algebra II
Finite-dimensional vector spaces (over R and C), subspaces, linear independence and bases. Linear transformations and matrices. Inner product spaces (over R and C); Orthonormal bases. Eigenvalues and diagonalization. Bilinear and quadratic forms; principal axis theorem.
Precludes additional credit for Mathematics 69.112.
Prerequisites: (i) Mathematics 69.114*, or a grade of C- or better in Mathematics 69.117* or 69.119*; and (ii) a grade of C- or better in Mathematics 69.107* or equivalent; or permission of the School.
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour tutorial.
Mathematics 69.218*
Abstract Algebra I
Sets and relations, number theory, group theory, ring theory, cardinal numbers.
Precludes additional credit for Mathematics 69.311* and 70.210.
Prerequisite: Mathematics 69.112 or 69.217*.
Lectures three hours a week and one hour tutorial.
Mathematics 69.244*
Ordinary Differential Equations I
Ordinary differential equations; applications; special first and second order types. Linear homogeneous and non-homogeneous equations with constant coefficients; variation of parameters; simple harmonic motion. Special linear equations with variable coefficients. Series solutions about ordinary points.
Precludes additional credit for Mathematics 69.105*, 69.201, 69.202, 70.244* and 70.260.
Prerequisites: Mathematics 69.102 and 69.112 (or 69.117* and 69.207*).
Lectures three hours a week and one hour tutorial.
Mathematics 69.257*
Introduction to Statistics
Data analysis; introduction to probability theory; some standard discrete and continuous distributions such as the binomial, Poisson, hypergeometric, normal, t, and chi-square; their application to interval estimation and significance testing; simple linear regression and correlation, contingency tables; testing for goodness-of-fit. Computational aspects of statistics.
Precludes additional credit for Mathematics 69.266*, 69.352*, Economics 43.220 and Geography 45.206*.
Prerequisite: An OAC in Mathematics or equivalent or permission of the School.
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour laboratory.
Note: See Note, p.334, under Graduation Regulations, regarding Economics 43.220.
Mathematics 69.259*
Computational Statistics
Exploratory data analysis, non-parametric methods, linear regression and correlation, basic experimental designs, related topics. Computer packages are used for statistical analyses.
Precludes additional credit for Mathematics 69.267*, 70.259*, and Economics 43.220.
Prerequisites: (i) Mathematics 69.257* and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*; or equivalents; or permission of the School.
See Deferred Final Examinations Note, p.336.
Lectures three hours a week and one hour laboratory.
Note: See Note, p.334, under Graduation Regulations, regarding Economics 43.220.
Mathematics 69.265*
Probability Models
Introductory probability theory. Introduction to stochastic modelling, Markov chains and queueing theory. Random number generation and Monte Carlo simulation. Statistical methods for fitting and evaluating models; estimation and testing. Applications to computer system performance evaluation, analysis of algorithms, reliability, search and decision problems.
Restricted to students in the Bachelor of Computer Science, Computer Mathematics and Computer Statistics programs.
Precludes additional credit for Mathematics 69.352*, 70.260 and 70.265*.
Prerequisites: Mathematics 69.207* (or 69.102) and 69.114* (or 69.117*).
Lectures three hours a week and one hour tutorial.
Mathematics 69.266*
Business Statistics I
Introduction to statistical computing; probability concepts; descriptive statistics; estimation and testing of hypotheses. Emphasis on the development of an ability to interpret results of statistical analyses with applications from business.
Restricted to students in the School of Business.
Precludes additional credit for Mathematics 69.257*, 69.352*, Economics 43.220 and Geography 45.206*.
Prerequisites: either: item (iii); or both of items (i) and (ii):
(i) Mathematics 69.109* with a grade of C- or better; and (ii) an OAC in Algebra and Geometry, or Mathematics 69.017*; (iii) Business 42.173 with a grade of C- or better; or equivalents.
Lectures three hours a week and one hour laboratory.
Mathematics 69.267*
Business Statistics II
Topics include: experimental design, multiple regression and correlation analysis, covariance analysis, and introductory time series. Use of computer packages.
Restricted to students in the School of Business.
Precludes additional credit for Mathematics 69.259*, 70.259* and Economics 43.220.
Prerequisite: Mathematics 69.266*.
Lectures three hours a week and one hour laboratory.
Mathematics 69.280*
Discrete Mathematics and Algorithms
An introduction to discrete mathematics and algorithms in the context of the computational sciences. Basic number theory and counting methods, algorithms for strings, trees and sequences. Applications to DNA and protein sequencing problems. Analysis and complexity of algorithms. (Also listed as Computational Sciences 68.280*.)
Only one of Mathematics 69.185* / Computer Science 95.185* or Mathematics 69.280* / Computational Sciences 68.280* may count for credit in a B.Math. program.
Prerequisites: Computer Science 95.106* and at least one of Mathematics 69.107*, 69.117*, or 69.257*.
Lectures three hours a week.
Mathematics 69.307*
Functions of a Complex Variable
Analytic functions, contour integration, residue calculus, conformal mapping. Intended for non-engineering students.
Precludes additional credit for Mathematics 69.376*, 70.307*, Physics 75.387* and 75.386.
Prerequisite: One of Mathematics 69.201, 69.202, 69.204*, 69.208* or 69.209*, or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 69.309*
Introductory Analysis
The real number system, sequences and series, functions of a single real variable, derivatives, the definite integral, uniform convergence.
Precludes additional credit for Mathematics 70.200.
Prerequisite: One of Mathematics 69.201, 69.202, 69.204*, 69.208*, 69.209*, or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 69.311*
Algebraic Structures with Computer Applications
Introduction to algebraic structures: groups, rings, fields, lattices, and Boolean algebras; with applications of interest to students in Computer Science.
This course may not be used to meet the 300-level course requirements in any Major or Honours program in Mathematics and Statistics.
Precludes additional credit for Mathematics 69.218* and 70.210.
Prerequisite: Mathematics 69.217*, or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 69.317*
Linear Algebra III
Similarity and unitary triangularization of matrices. Direct methods of solving a system of linear equations. Iterative techniques. Bounds for eigenvalues. Power method and deflation techniques of approximation. The emphasis of the course is primarily on computational aspects.
Prerequisites: (i) a grade of C- or better in Mathematics 69.112 or 69.217*; and (ii) credit in Mathematics 69.102 or 69.207*; or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 69.318*
Abstract Algebra II
Groups and rings. Permutations. Finite symmetry groups. Polynomials, unique factorization domains. Quotient rings, ideals. Field extensions, finite fields. Polynomial equations. Geometric constructions - three famous problems: duplication of the cube; trisection of an arbitrary angle; quadrature of the circle.
Precludes additional credit for Mathematics 70.316*, 70.318*, and 70.310.
Prerequisite: Mathematics 69.218*, or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 69.325*
Euclidean Geometry and its Groups
Transformations of the Euclidean plane (isometries, similarities); solutions of geometric problems using these transformations; groups of symmetries of finite plane figures, frieze patterns, and regular polyhedra; inversion and the extension to the inversive plane; problems solved using inversion; orthogonal circles and pencils of coaxial circles.
Prerequisite: Mathematics 69.218*.
Lectures three hours a week and one hour tutorial.
Mathematics 69.326*
Plane Projective Geometry
Axioms of Desarguesian geometry, principle of duality; projectivities, perspectivities, and the fundamental theorem; collineations (homologies and elations); correlations (polarities and conics); algebraic model; introduction to finite projective planes.
Precludes additional credit for Mathematics 70.326*.
Prerequisite: Mathematics 69.218*.
Lectures three hours a week and one hour tutorial.
Mathematics 69.344*
Ordinary Differential Equations II
Series solutions of ordinary differential equations of second order about regular singular points; asymptotic solutions. Systems of ordinary differential equations of first order; matrix methods. Existence and uniqueness theorems. Nonlinear autonomous systems of order 2; qualitative theory. Numerical solutions of ordinary differential equations.
Precludes additional credit for Mathematics 70.308*.
Prerequisites: Mathematics 69.244*, 69.208*; and 69.112 or 69.217*.
Lectures three hours a week and one hour tutorial.
Mathematics 69.352*
Probability and Statistics
Axioms of probability; conditional probability and independence; random variables; distributions: binomial, Poisson, hypergeometric, normal, gamma; central limit theorem; sampling distributions; point estimation: maximum likelihood, and method of moments; confidence intervals; testing of hypotheses: one and two populations; engineering applications: acceptance sampling, control charts, reliability.
Restricted to students in the Faculty of Engineering, or in B.Sc.(Honours) in Applied Physics.
This course may not be used to meet the 300-level course requirements in any Major or Honours program in Mathematics and Statistics.
Precludes additional credit for Mathematics 69.257*, 69.265*, 69.266*, Economics 43.220 and Geography 45.206*.
Prerequisite: Mathematics 69.204*, or 69.201.
Lectures three hours a week and one hour laboratory.
Mathematics 69.353*
Regression Analysis
Review of simple and multiple regression with matrices, Gauss-Markov theorem, polynomial regression, indicator variables, residual analysis, weighted least squares, variable selection techniques, nonlinear regression, correlation analysis and autocorrelation. Computer packages are used for statistical analyses.
Precludes additional credit for Mathematics 70.355*, Economics 43.476*, and for Mathematics 69.351; Psychology 49.300 is precluded for additional credit for students registered in a Mathematics program.
Prerequisites: (i) Mathematics 69.259* or 69.267*, or Economics 43.220, or equivalent; and (ii) Mathematics 69.112 or 69.117* or 69.119* or equivalent; or permission of the School.
Lectures three hours a week and one hour laboratory.
Mathematics 69.354*
Analysis of Variance and Experimental Design
Single and multifactor analysis of variance, orthogonal contrasts and multiple comparisons, analysis of covariance; nested, crossed and repeated measures designs; completely randomized, randomized block, Latin squares, factorial experiments, related topics. Computer packages are used for statistical analyses.
Precludes additional credit for Mathematics 70.355*, and for Mathematics 69.351; Psychology 49.300 is precluded for additional credit for students registered in a Mathematics program.
Prerequisite: Mathematics 69.353* or permission of the School.
Lectures three hours a week and one hour laboratory.
Mathematics 69.357*
Sampling Methodology
The sample survey as a vehicle for information collection in government, business, scientific and social agencies. Topics include: planning a survey, questionnaire design, simple random, stratified, systematic and cluster sampling designs, estimation methods, problem of non-response, related topics.
Prerequisite: One of Mathematics 69.257*, or 69.259*, 69.266*, 69.267*, Economics 43.220 or equivalent; or permission of the School.
Lectures three hours a week and one hour laboratory.
Mathematics 69.358*
Elements of Probability Theory
Discrete and continuous distributions; moment-generating functions, marginal and conditional distributions, transformation theory, limiting distributions.
Precludes additional credit for Mathematics 69.350, 70.350, and 70.358*.
Prerequisites: (i) Mathematics 69.208* [or one of 69.201, 69.202, 69.204*, or 69.209*]; and (ii) one of Mathematics 69.257*, 69.266*, Economics 43.220; or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 69.359*
Mathematical Statistics
Point and interval estimation, sufficient statistics, hypothesis testing, chi-square tests with enumeration data.
Precludes additional credit for Mathematics 69.350, 70.350, and 70.359*.
Prerequisite: Mathematics 69.358* or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 69.368*
Probability in Communications and Electrical Engineering
Probability models and basic concepts; independence and conditional probabilities; discrete, continuous and multiple random variables; distribution and density functions; expectations and moments; sums of random variables; elementary statistics; introduction to random processes; applications to areas such as communication systems and networks.
Restricted to students in the Faculty of Engineering.
Precludes additional credit for Mathematics 69.358* and 70.358*.
Prerequisite: Mathematics 69.204*, or equivalent.
Lectures three hours a week, tutorial one hour a week.
Mathematics 69.375*
Mathematical Methods I
Laplace transforms, Fourier series and Fourier transforms, solutions of partial differential equations of mathematical physics, boundary value problems, applications.
This course may be taken for credit as a 300-level Honours Mathematics course, by students in any Honours program in the School of Mathematics and Statistics.
Precludes additional credit for Mathematics 69.304*, Physics 75.388*, and 75.386.
Prerequisite: Mathematics 69.201 or 69.202; or (i) Mathematics 69.244* or 69.105*, and (ii) Mathematics 69.204* or 69.208* or 69.209*; or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 69.380*
Modelling and Computational Methods for Experimental Science
Mathematical modelling in the experimental sciences: design, analysis and pitfalls. Computational methods directly applicable to problems in science will be described, including: function evaluation, interpolation, solution of linear equations, root finding, integration, solution of differential equations, Fourier series and Monte Carlo methods. (Also listed as Computational Sciences 68.380*.)
Only one of Mathematics 69.386* / Computer Science 95.386* or Mathematics 69.380* / Computational Sciences 68.380* may count for credit in a B.Math. program.
Prerequisites: Mathematics 69.117*; 69.207* or 69.209*; and Computer Science 95.106*.
Lectures three hours a week.
Mathematics 69.381*
Linear Programming
Formulation of linear programming problems, the simplex method, duality theory, implementations, extensions and applications. Network flow problems and the network simplex method.
Precludes additional credit for Economics 43.404*, Engineering 94.320*.
Prerequisite: Mathematics 69.112 or 69.217*, or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 69.382*
Combinatorial Optimization
Network flow algorithms: max flow, min cost flow. Connections to linear programming. Optimal matching. Heuristic algorithms for tour problems.
Prerequisite: Mathematics 69.112 or 69.217* or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 69.384*
Design and Analysis of Algorithms I
An introduction to the design and analysis of algorithms. Topics include: recurrence relations, sorting and searching, divide-and-conquer, dynamic programming, greedy algorithms, amortized analysis. (Also listed as Computer Science 95.384*.)
Prerequisites: Computer Science 95.202*, and either 95.285* or both of Mathematics 69.207* and 69.218* or equivalents.
Lectures three hours a week.
Mathematics 69.386*
Numerical Analysis
Elementary discussion of error, polynomial interpolation, quadrature, linear systems of equations and matrix inversion, non-linear equations, difference equations and ordinary differential equations. (Also listed as Computer Science 95.386*.)
Prerequisites: (i) Mathematics 69.102, 69.105* or 69.207* (or 69.201 or 69.202); and (ii) Mathematics 69.112 or 69.217*; and (iii) knowledge of a computer language.
Lectures three hours a week and one hour tutorial.
Mathematics 69.387*
Mathematical Software
Incorporation of basic numerical methods into efficient, reliable software. The course includes examination of existing software systems, e.g., linear systems, non-linear systems, optimization, or differential equations. (Also listed as Computer Science 95.387*.)
Prerequisite: Mathematics 69.386*.
Lectures three hours a week and one hour tutorial.
Mathematics 69.389*
Introduction to Number Theory and Cryptography
Congruences, distribution of primes, general cryptographic systems, public key cryptographic systems and authentification using number theory, primality testing and factoring in relation to cryptography, continued fractions and diophantine equations.
Prerequisites: Mathematics 69.218* or 69.311* or 70.210; knowledge of a computer language.
Lectures three hours a week and one hour tutorial.
Mathematics 69.397*
Directed Studies
Available only to students whose program requires a 0.5 credit not offered by the School of Mathematics and Statistics.Mathematics Courses for Honours Students
Note: Students who have completed Mathematics 69.208* or 69.204*, and/or Mathematics 69.218* or 69.311*, with good grades, and who wish to transfer to an honours program in Mathematics and Statistics should consult the Undergraduate Advisor of the School.Mathematics 70.200
Calculus and Introductory Analysis
Higher dimensional calculus, chain rule, gradient, line and multiple integrals with applications. Use of implicit and inverse function theorems. Real number axioms, limits, continuous functions, differentiability, infinite series, uniform convergence, the Riemann integral.
Precludes additional credit for Mathematics 69.204*, 69.208*, 69.209*, 69.309*, and for 69.201, 69.202.
Prerequisites: (i) Mathematics 69.102 or 69.207*; and (ii) Mathematics 69.112 or 69.117*; or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 70.210
Algebra
Set theory, algebraic systems, vector spaces, inner product spaces, linear transformations, determinants, quadratic forms, selected applications.
Precludes additional credit for Mathematics 69.218* or 69.311*.
Prerequisite: Mathematics 69.112 or 69.217*.
Lectures three hours a week and one hour tutorial.
Mathematics 70.220*
Co-operative Work Term Report 1
On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.
Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.
Mathematics 70.244*
Ordinary Differential Equations
Ordinary differential equations of the first and second order, existence and uniqueness of solutions; numerical solutions, error analysis; linear systems of first order; difference equations; higher order linear equations. Modelling with differential equations. A mathematical computer software package will be used.
Precludes additional credit for Mathematics 69.105*, 69.201, 69.202, 69.244*, 70.260.
Prerequisites: Mathematics 69.102 (or 69.207*) and 69.112 (or 69.217*).
Lectures three hours a week, tutorial one hour a week.
Mathematics 70.259*
Statistics: Theory and Practice
Computational and inferential statistics; basic distributions (normal, t, chi-square, F); maximum likelihood and moment estimators; properties of estimators; confidence intervals (one- and two-sample procedures); testing of simple and composite hypotheses; regression and analysis of variance models; non-parametric procedures; contingency tables. Use of computer packages.
Precludes additional credit for Mathematics 69.259*, 69.267*, Economics 43.220.
Prerequisite: Mathematics 70.265* or 70.260.
Lectures three hours a week and one hour tutorial/laboratory.
Mathematics 70.265*
Introduction to Probability with Applications
Axioms of probability, basic combinatorial analysis, conditional probability and independence, discrete and continuous random variables, joint and conditional distributions, expectation, central limit theorem, sampling distributions, simulation and applications to descriptive statistics. A statistical software package will be used.
Precludes additional credit for Mathematics 69.265* and 70.260.
Prerequisites: Mathematics 69.102 (or 69.207*) and 69.112 (or 69.217*).
Lectures three hours a week, tutorial one hour a week.
Mathematics 70.297*
Directed Studies
Available only to Honours students whose program requires a 0.5 credit not offered by the School of Mathematics and Statistics.
Mathematics 70.301*
Real Analysis
Metric spaces; limits, continuity, open and closed sets, compactness, connectedness and completeness. Uniform convergence of sequences of functions, as convergence in metric spaces of bounded and continuous functions. Weierstrass approximation theorem. Contraction mappings and applications to integral and differential equations.
Prerequisite: Mathematics 70.200 or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 70.302*
Advanced Calculus
Vector fields on surfaces. The functions div, curl and grad. Line and surface integrals. The divergence theorem and Stokes' theorem. Exterior algebra. Stokes' formula. Functions of bounded variation. The Riemann-Stieltjes integral.
Prerequisite: Mathematics 70.200 or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 70.307*
Functions of a Complex Variable
Analytic functions, contour integration, residue calculus, conformal mapping. Precludes additional credit for Mathematics 69.307*, 69.376*, Physics 75.387*, and 75.386.
Prerequisite: Mathematics 70.200 or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 70.308*
Ordinary Differential Equations
Analytic ordinary differential equations: series solutions of ordinary differential equations about ordinary and regular singular points. Asymptotic solutions. Sturm-Liouville theory. Bessel and Legendre functions. Fourier series.
Precludes additional credit for Mathematics 69.344*, Physics 75.388*, and 75.386.
Prerequisites: Mathematics 70.200; and 70.244* or 70.260.
Lectures three hours a week and one hour tutorial.
Mathematics 70.316*
Introduction to Group Theory
Homomorphism theorems; groups acting on sets; permutation groups and groups of matrices; Sylow theory for finite groups; finitely generated abelian groups; generators and relations; applications.
Precludes additional credit for Mathematics 70.310 and 69.318*.
Prerequisite: Mathematics 70.210, or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 70.318*
Rings and Fields
Rings; integral domains; Euclidean and principal ideal domains; polynomial rings over a field; modules over principal ideal domains and applications; fields; algebraic extensions of fields; finite fields; applications.
Precludes additional credit for Mathematics 70.310 and 69.318*.
Prerequisite: Mathematics 70.210, or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 70.320*
Co-operative Work Term Report 2
On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.
Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.
Mathematics 70.321*
Co-operative Work Term Report 3
On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.
Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.
Mathematics 70.326*
Foundations of Projective Geometry
Definition of a general projective plane and immediate consequences; finite planes (combinatorial results, sub-planes, incidence matrices) and planar ternary rings; collineations, role of Desargues' configuration, examples of types of planes.
Precludes additional credit for Mathematics 69.326*.
Prerequisite: Mathematics 70.210.
Lectures three hours a week and one hour tutorial.
Mathematics 70.336*
Elements of Set Theory
Axioms of set theory. Development of the systems of natural numbers and the real numbers. Axiom of choice, Zorn's lemma, well-ordering. The Schröder-Bernstein theorem, cardinal numbers, ordinal numbers, transfinite induction, cardinal and ordinal arithmetics.
Prerequisite: Mathematics 70.210 or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 70.346*
Autonomous Dynamical Systems
Basic concepts of dynamical systems. Stability; limit cycles; Lyapunov's direct method. Theory of autonomous dynamical systems. Volterra systems; principle of competitive exclusion in population biology. The threshold theorem of epidemiology. Basic concepts of nonequilibrium statistical mechanics.
Prerequisites: Mathematics 70.200; and 70.244* or 70.260.
Lectures three hours a week and one hour tutorial.
Mathematics 70.355*
Regression and Experimental Design
Linear regression - theory and methods; design of experiments - analysis of the completely randomized, randomized block and Latin square designs; multiple comparisons; factorial experiments; related topics.
Precludes additional credit for Mathematics 69.353*, 69.354*, Economics 43.476*, and for Mathematics 69.351. Psychology 49.300 is precluded for additional credit for students registered in a Mathematics program.
Prerequisites: (i) Mathematics 70.259* or 69.259*; and (ii) 69.112 or 69.217*; or permission of the School.
Lectures three hours a week and one hour laboratory.
Mathematics 70.356*
Stochastic Processes and Queueing Theory
Stochastic modelling, Markov chains, birth and death processes, renewal theory. Queueing theory: analytical and simulation methods. Applications to computer systems, operations research and social sciences.
Prerequisites: Mathematics 70.265* or 70.260; or a GPA of 6.0 or better over the three courses Mathematics 69.207*, 69.217* (or 69.112), and 69.265*; or permission of the School.
Lectures three hours a week and one hour tutorial.
Mathematics 70.358*
Elements of Probability Theory
Random variables and moment-generating functions, concepts of conditioning and correlation; laws of large numbers, central limit theorem; multivariate normal distribution; distributions of functions of random variables, sampling distributions, order statistics.
Precludes additional credit for Mathematics 69.358*, 69.350, 70.350.
Prerequisites: (i) Mathematics 70.265* (or 69.265* or 70.260); and (ii) Mathematics 70.200 (or a grade of C+ or better in 69.208*); or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 70.359*
Mathematical Statistics
Empirical distribution functions, Monte Carlo methods, elements of decision theory, point estimation, interval estimation, tests of hypotheses, robustness, nonparametric methods.
Precludes additional credit for Mathematics 69.350, 69.359*, 70.350.
Prerequisite: Mathematics 70.358* or permission of the School.
Lectures three hours a week, tutorial one hour a week.
Mathematics 70.385*
Discrete Structures and Applications
Enumeration: elementary methods, inclusion and exclusion, recurrence relations, generating functions and applications. Graph theory and algorithms: connectivity, planarity, Hamilton and Euler paths.Error-correcting codes. (Also listed as Computer Science 95.385*.)
Prerequisite: One of Mathematics 69.218*, 69.311*, or 70.210.
Lectures three hours a week and one hour tutorial.
A selection of courses in the 400 series will be offered.
Mathematics 70.403*
Functional Analysis
Banach spaces and bounded linear operators, Hahn-Banach extension and separation, dual spaces, bounded inverse theorems, uniform boundedness principle, applications. Compact operators. Differential calculus in Banach spaces, inverse and implicit function theorems and their application to differential equations. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.508, for which additional credit is precluded.
Prerequisite: Mathematics 70.301* or permission of the School.
Lectures three hours a week.
Mathematics 70.407*
Measure and Integration Theory
Lebesgue measure and integration on the real line; sigma algebras and measures; integration theory; Lp spaces; Fubini's theorem; decomposition theorems and Radon-Nikodym derivatives. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.507, for which additional credit is precluded.
Prerequisite: Mathematics 70.301* or 70.302* or permission of the School.
Lectures three hours a week.
Mathematics 70.415*
Rings and Modules
Fundamental concepts in rings and modules, structure theorems, applications.
Prerequisite: Mathematics 70.318* or 70.310 or permission of the School.
Lectures three hours a week.
Mathematics 70.416*
Group Theory
Fundamental principles as applied to abelian, nilpotent, solvable, free and finite groups; representations. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.516, for which additional credit is precluded.
Prerequisite: Mathematics 70.316* or 70.310 or permission of the School.
Lectures three hours a week.
Mathematics 70.417*
Commutative Algebra
Fields, including algebraic and transcendental extensions, Galois theory, valuation theory; Noetherian commutative rings, including Noether decomposition theorem and localization.
Prerequisite: Mathematics 70.318* or 70.310 or permission of the School.
Lectures three hours a week.
Mathematics 70.418*
Homological Algebra and Category Theory
Axioms of set theory; categories, functors, natural transformations; free, projective, injective and flat modules; tensor products and homology functors, derived functors; dimension theory. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.518, for which additional credit is precluded.
Prerequisite: Mathematics 70.318* or 70.310 or permission of the School.
Lectures three hours a week.
Mathematics 70.419*
Fields and Coding Theory
Introduction to field theory, emphasizing the structure of finite fields, primitive elements and irreducible polynomials. The influence of computational problems will be considered. Theory and applications of error-correcting codes: algebraic codes, convolution codes, decoding algorithms, and analysis of code performance.
Prerequisite: Mathematics 70.210, or 69.311* or 69.218* or equivalent; or permission of the School.
Lectures three hours a week.
Mathematics 70.420*
Co-operative Work Term Report 4
On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.
Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.
Mathematics 70.421*
Co-operative Work Term Report 5
On completion of the work term, the student must submit to the School of Mathematics and Statistics a written report on the work performed. Graded Sat or Uns.
Prerequisites: Registration in the Co-operative Education Option of an Honours program offered by the School of Mathematics and Statistics, and permission of the School.
Mathematics 70.425*
Introduction to General Topology
Topological spaces, maps, subspaces, product and identification topologies, separation axioms, compactness, connectedness. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.525, for which additional credit is precluded.
Prerequisite: Mathematics 70.301* or permission of the School.
Lectures three hours a week.
Mathematics 70.426*
Introduction to Algebraic Topology
An introduction to homotopy theory. Topics include the fundamental group, covering spaces and the classification of two-dimensional manifolds. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.526, for which additional credit is precluded.
Prerequisites: Mathematics 70.316* (or 70.310) and 70.425*; or permission of the School.
Lectures three hours a week.
Mathematics 70.427*
Foundations of Geometry
A study of at least one modern axiom system of Euclidean and non-Euclidean geometry, embedding of hyperbolic and Euclidean geometries in the projective plane, groups of motions, models of non-Euclidean geometry.
Prerequisite: Mathematics 70.316* (may be taken concurrently) or 70.310, or permission of the School.
Lectures three hours a week.
Mathematics 70.428*
Introduction to Differentiable Manifolds
A study of differentiable manifolds from the point of view of either differential topology or differential geometry. Topics such as smooth mappings, transversality, intersection theory, vector fields on manifolds, Gaussian curvature, Riemannian manifolds, differential forms, tensors and connections are included.
Prerequisite: Mathematics 70.301* or permission of the School.
Lectures three hours a week.
Mathematics 70.435*
Analytic Number Theory
Dirichlet series, characters, Zeta-functions, prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, binary quadratic forms. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.535, for which additional credit is precluded.
Prerequisite: Mathematics 70.307* or permission of the School.
Lectures three hours a week.
Mathematics 70.436*
Algebraic Number Theory
Algebraic number fields, bases, algebraic integers, integral bases, arithmetic in algebraic number fields, ideal theory, class number. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.536, for which additional credit is precluded.
Prerequisite: Mathematics 70.318* (may be taken concurrently) or 70.310, or permission of the School.
Lectures three hours a week.
Mathematics 70.447*
Tensor Analysis and Relativity Theory
Development of tensor analysis, application to Riemannian spaces and relativity theory.
Prerequisites: Mathematics 70.345* and 70.346* or permission of the School.
Lectures three hours a week.
Mathematics 70.450*
Parametric Estimation
Preliminaries on probability theory; exact and asymptotic sampling distributions; unbiasedness, consistency, efficiency, sufficiency and completeness; properties of maximum likelihood estimators; least squares estimation of location and scale parameters based on order statistics and sample quantiles; Best Asymptotically Normal (BAN) estimators. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.560, for which additional credit is precluded.
Prerequisite: Mathematics 70.350 or 70.359* or permission of the School.
Lectures three hours a week.
Mathematics 70.451*
Probability Theory
Introduction to probability, characteristic functions, probability distributions, limit theorems.
Prerequisites: Mathematics 70.356* and 70.358* or permission of the School.
Lectures three hours a week.
Mathematics 70.452*
Survey Sampling
Basic concepts in sampling from finite populations; simple random sampling; stratified sampling; choice of sampling unit; cluster and systematic sampling; introduction to multistage sampling; ratio estimation; sampling with unequal probabilities and with replacement; replicated sampling; related topics.
Prerequisites: (i) Mathematics 70.259* or 69.259*; and (ii) either 70.359* (or 70.350) or a grade of C+ or better in 69.359* (or 69.350); or permission of the School.
Lectures three hours a week.
Mathematics 70.453*
Applied Multivariate Analysis
Selected topics in regression and correlation non-linear models. Multivariate statistical methods, principal components, factor analysis, multivariate analysis of variance, discriminant analysis, canonical correlation, analysis of categorical data. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.559, for which additional credit is precluded.
Prerequisites: Mathematics 70.355*; or 69.359* (or 69.350) and 69.354*; or permission of the School.
Lectures three hours a week.
Mathematics 70.456*
Non-Parametric Methods
Order statistics; rank statistics; permutations; asymptotics; hypothesis of randomness; stochastic ordering; Wilcoxon test; median test; Kolmogorov-Smirnov test; hypothesis of symmetry and random blocks; independence hypothesis; treatment of ties; power and efficiency. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.556, for which additional credit is precluded.
Prerequisite: Mathematics 70.359* (or 70.350) or permission of the School.
Lectures three hours a week.
Mathematics 70.457*
Statistical Inference
Sufficient statistics, simple and composite hypotheses, most powerful and similar region test, distribution-free tests, confidence intervals, goodness-of-fit and likelihood ratio tests, large sample theory, Bayesian and likelihood methods, sequential tests. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.551, for which additional credit is precluded.
Prerequisite: Mathematics 70.450* or permission of the School.
Lectures three hours a week.
Mathematics 70.458*
Stochastic Models
Review of discrete Markov chains and Poisson processes; pure jump Markov processes including the Q-matrix approach; the Kolmogorov equations; classification of states; stationary and limiting distributions; renewal theory. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.571, for which additional credit is precluded.
Prerequisite: Mathematics 70.356* or permission of the School.
Lectures three hours a week.
Mathematics 70.459*
Advanced Mathematical Modelling
Real life situations in the physical, social, and life sciences are often modelled using mathematical tools. This course will examine various models and techniques used in their analysis, e.g., matrix procedures in connection with population models. Students will use a computer package to obtain numerical results. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.561, for which additional credit is precluded.
Prerequisites: Mathematics (i) 70.244* and 70.265* (or 70.260; or 69.244* and 69.265*) and (ii) 70.356*; or permission of the School.
Lectures three hours a week.
Mathematics 70.460*
Case Studies in Operations Research
Applications of the principles of Operations Research to practical problems in business, management, and science. Students present at least one case and analyze cases in the published literature. Cases may also be presented by visiting practitioners.
Note: this course is designed for students in their final year in Honours Operations Research. Students in Honours Mathematics/Statistics programs may only take this course as a free option.
Prerequisites: Mathematics 69.259* (or 70.259*) and 69.381*; or permission of the School.
Seminars three hours a week.
Mathematics 70.470*
Partial Differential Equations
First order linear, quasi-linear, and non-linear equations; second order equations in two and more variables; systems of equations; the wave equation; Laplace and Poisson equations, Dirichlet and Neumann problems; Green's functions. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.546, for which additional credit is precluded.
Prerequisites: Mathematics 70.308* and one of 70.302* or 70.307* or permission of the School.
Lectures three hours a week.
Mathematics 70.471*
Topics in Partial Differential Equations
Theory of distributions, initial-value problems based on 2-dimensions wave equations, Laplace transform, Fourier integral transform, diffusion problems, Helmholtz equation with application to boundary and initial-value problems in cylindrical and spherical coordinates. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.547, for which additional credit is precluded.
Prerequisites: Mathematics 70.308* and one of 70.302* or70.307* or permission of the School.
Lectures three hours a week.
Mathematics 70.472*
Integral Transforms
Laplace, Fourier, Hankel and Mellin transforms, selection of a suitable transform for a given partial differential equation boundary value problem. Operational properties of transforms. Inversion theorems. Approximate evaluation of inversion integrals for small and large values of parameter. Application to the solution of integral equations.
Prerequisite: Mathematics 70.307* or permission of the School.
Lectures three hours a week.
Mathematics 70.473*
Qualitative Theory of Ordinary Differential Equations
Ordinary differential equations: existence-uniqueness theorems, vector formulation for systems; stability theory, Lyapunov theorems, perturbation theorems and structural stability; Poincaré-Bendixon theory.
Prerequisites: Mathematics 70.301*, 70.308*, 70.346*.
Lectures three hours a week.
Mathematics 70.481*
Topics in Combinatorics
An in-depth study of one or more topics from: generating functions, Polya's theory of counting, block designs, coding theory, partially ordered sets and Ramsey theory.
Prerequisites: Mathematics 70.210 and 70.385* or permission of the School.
Lectures three hours a week.
Mathematics 70.482*
Introduction to Mathematical Logic
Symbolic logic, propositional and predicate calculi, set theory and model theory, completeness.
Prerequisite: Mathematics 70.210 or permission of the School.
Lectures three hours a week.
Mathematics 70.483*
Computable Functions
Recursive functions and computability, algorithms, Church's thesis, Turing machines, computational logic, NP-completeness. (Also listed as Computer Science 95.483*.)
Prerequisite: Mathematics 70.210 or 70.385* or permission of the School.
Lectures three hours a week.
Mathematics 70.485*
Theory of Automata
Finite automata and regular expressions, properties of regular sets, context-free grammars, pushdown automata, deterministic context-free languages. Turing machines, the Chomsky hierarchy. Undecidability, intractable problems. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.565, for which additional credit is precluded. (Also listed as Computer Science 95.485*.)
Prerequisite: Mathematics 70.385* or 70.316* or 70.318* (or 70.310) or permission of the School.
Lectures three hours a week.
Mathematics 70.486*
Numerical Linear Algebra
Study of matrix inversion techniques; techniques of finding eigenvalues and eigenvectors, solution of systems of linear equations; direct and indirect methods, their comparison and error analysis; applications in optimization and other areas. (Also listed as Computer Science 95.486*.)
Prerequisites: Mathematics 69.112 or 69.217*; and Mathematics 70.200 or 69.309*, or permission of the School.
Lectures three hours a week.
Mathematics 70.487*
Game Theory
Two-person zero-sum games; infinite games; multistage games; differential games; utility theory; two-person general-sum games; bargaining problem;
n-person games; games with a continuum of players. Also offered at the graduate level, with additional or different requirements, as Mathematics 70.567, for which additional credit is precluded.
Prerequisite: Mathematics 70.301* or permission of the School.
Lectures three hours a week.
Mathematics 70.488*
Graph Theory and Algorithms
Paths, circuits, Eulerian and Hamiltonian graphs, connectivity, colouring problems, matching, Ramsey theory, network flows.
Prerequisites: Mathematics 70.385* or 70.316* or 70.318* (or 70.310) or permission of the School.
Lectures three hours a week.
Mathematics 70.489*
Mathematical Cryptography
Topics covered include: a general survey of public key cryptography; classical applications of finite fields and number theory; relevant background in geometry and algebraic curves; computational issues concerning elliptic curves; elliptic curve cryptosystems; security issues.
Prerequisite: Mathematics 69.389*, or permission of the School.
Lectures three hours a week.
Mathematics 70.495*
Honours Project
Consists of a written report on some approved topic or topics in the field of mathematics, together with a short lecture on the report.
Prerequisite: B.Math.(Honours) students only, see p. 326.
Note: Each student should commence work on the Honours Project under a faculty supervisor before June 1 of the year before he or she intends to graduate (for full-time students, this would be the June 1 between Third and Fourth Year). The first draft of the report must be submitted to the supervisor by November 1, and the final draft to the School by January 15. Students who do not meet this latter deadline will be given the grade F.Mathematics 70.496*
Directed Studies
Prerequisite: B.Math.(Honours) students only.
Mathematics 70.497*
Directed Studies
Prerequisite: B.Math.(Honours) students only.
Carleton
University
2001-2002 Undergraduate Calendar
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