30 courses in the 1985–86 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Elementary principles of enumeration. Principle of inclusion-exclusion, generating functions, recurrence equations. Elementary graph theory and graphical
algorithms. Introduction to design theory.
Credit will be granted for only 1 of C&O 220, 230. C&O 220 cannot be counted for credit toward a BMath Honours degree.
Offered at St. Jerome’s College.
Introduction to the combinatorics of ordinary generating functions. Introduction to basic graph theory and graphical algorithms.
Prereq: MATH 130b, 134b
Credit will be granted for only 1 of C&O 220, 230.
Structure and classification of optimization problems. The concepts of algorithm and heuristic. Continuous models. Linear models. Methods of branch-and-bound, implicit enumeration and approximation. Applications.
Prereq: MATH 130b, 134b '
Students may not enrol in C&O 270 if they have previously completed, or are concurrently enrolled in, C&O 350 or 367.
Also offered at St. Jerome's College in Fall term.
The combinatorics of ordinary and
exponential generating functions. Matrix
methods, and decompositions. The
Lagrange theorem. Applications to
enumeration of sequences, trees.
covers, lattice. paths and partitions. Prereq: C&O 230
A first course in error-correcting codes. Linear block codes, Hamming-Golay codes and multiple error-correcting BCH codes are studied. Various encoding and decoding schemes are considered. Prereq: MATH 224b Offered at St. Jerome's College.
An introduction to the‘ideas, methods
and applications of graph theory.
Finding shortest paths and maximum
matchings in weighted graphs. Deter-
mining the connectivity of a graph. Prereq: MATH 224a, C&O 230
A continuation of C&O 342. Planar graphs and embeddings in other surfaces. Vertex, edge and face colourings. The four-colour problem. Hamilton cycles. Applications to scheduling problems.
Prereq: C&O 342
A first course in problem formulation - and solution techniques in linear programming. The simplex and revised simplex methods. Active set formulation of the simplex method. Theory and applications of duality theory. Sensitivity Analysis.
Prereq: MATH 224a
Course Descriptions Mathematics.
Review of linear programming. Shortest path problems. The max-flow and minimum cost-flow problems. A study of the network simplex, augmentation and out-of-kilter algorithms. Applications to problems of transportation, distribution, man-job assignments and critical-path planning.
Prereq: C&O 350
Vector calculus with applications to Newton's method and method of steepest descent. One-dimensional optimization. Introduction to constrained optimization, including the elements of Kuhn-Tucker theory and Lagrange multipliers.
Prereq: MATH 2208, 224a
An applications-oriented course that illustrates how various mathematical models and methods of optimization can be used to solve problems arising in business, industry and science.
Prereq: C&O 350
An introduction to the use of probabilistic models in operations research. Techniques and applications of queueing theory, inventory theory and reliability theory.
Prereq: STAT 221
A course in problem solving. 100 problems are studied. Problems are taken mainly from the elementary parts of algebra, geometry, number theory, combinatorics and probability.
Prereq: MATH 130b, 134a/b. (220b, 224b, are recommended)
Although the mathematics for this course is technically elementary, the course is intended for third and faurthyear students, and the mathematical maturity of a senior student will be assumed.
Mathematics: Combinatorics and Optimization
An introduction to the combinatorial - aspects of the real plane. Main topics covered are the enumeration of various combinatorial objects in the plane, Sylvester's Triad Problem, Pick’s Theorem, partitioning the interior of a rectangle into squares of different sizes, an introduction to the theory of convex sets in the plane. Helly’s theorem and certain ramifications will be explored. Prereq: MATH 130b, 134a/b Although the mathematics for this course is technically elementary, the course is intended for third and fourthyear students, and the mathematical maturity of a senior student will be assumed. Offered at St. Jerome's College.
The course is an extension of C&O 330. The combinatorics of Eulerian generating functions, continued fractions, orthogonal polynomials and the ring of formal Laurent series. Enumeration under group action. Prereq: C&O 330
Topics covered include error correcting codes, resolvable designs, affine designs, weighing matrices, and their. interaction..
Prereq: MATH 324
A course covering a number of applications of computers to combinatorial problems. General procedures — backtrack programming, generation of permutations, partitions etc., as well as the solution of many specific problems. includes an introduction to computational complexity.
Prereq: C&O 230
An undergraduate seminar in combinatorics. The primary objective is to study current work in specific areas of combinatorics. Course content may vary from term to term.
Freiog: Consent of instructor
An in-depth study of 1 or 2 topics in graph theory. Course content may vary from term to term. Topics may include Planar graphs, extremal graph theory, directed graphs, enumeration, algebraic graph theory, probabilistic graph theory, connectivity, graph embedding, colouring problems.
Prereq: C&O 342 or consent of instructor
Packing, covering and partitioning prablems. Integer programming. Good algorithms for optimum assignments, matchings, flows, anti-chains and connectivity. Paths, trees and flowers. Min-max relations. Convexification of discrete problems. Vertices and facets of convex polyhedra. The concepts of NP and co-NP. Reducing NP problems to integer programming.
Prereq: C&O 351
A study of several techniques for solving integér (linear) programming problems. Cutting planes, implicit enumeration. branch-and-bound. Introduction to Boolean and pseudo-Boolean programming. Applications to problems of optimum routing, site location, set covering and packing, logic and lattice theory.
Prereq: C&O 351
Sequencing algorithms for scheduling tasks on single machines, paraliei machines, and flow shops. Applications to scheduling computers and manufacturing facilities. Combinatorial techniques used in algorithm development and convergence proofs.
Prereq: C&O 351 or 370
An introduction to the analysis, through appropriate mathematical models, of competitive situations such as those arising in social, economic, political or military conflict. Emphasis is placed on ‘the theory of two-person games.
Prereq: C&O 350.
16.95
Methods for the minimization and maximization of piecewise linear functions and linear functions subject to linear constraints, with applications to linear programming and data fitting. Emphasis is on algorithms, numerical considerations and software implementation.
Prereq: One of C&O 350, CS 337, 375 or consent of instructor
Cross-listed as CS 473.
An undergraduate seminar in optimization. The primary objective is to study recent work in specific areas of optimization. Course content may vary from term to term.
Prereq: Consent of instructor
A detailed presentation of optimatity conditions and effective algorithms for the solution of a quadratic programming problem. All concepts are developed as natural extensions of their counterparts in linear programming. Applications from portfolio analysis, engineering plasticity, regression, pattern recognition.
Prereq: C&O 350
Geometry and numerical algorithms of noniinear optimization. Variable metric and conjugate gradient methods. Convex programming. Feasible and nonfeasible direction methods. Recursive quadratic programming, nonorthogonal projections and active set strategies.
Prereq: C&O 350, 367
Topics include: famous construction problems, Mascheroni’s theorem, amicable pairs, perfect numbers and related numbers, Pythagorean triples; some of Archimedes’ great accomplishments: squaring the parabola; estimation of pi; Archimedes’ “Method”, the volume of the sphere; inscribed regular polygons.
Prereq: MATH 130b, 134a/b (220b and 224b are recommended)
Although the mathematics for this course is technically elementary, the course is intended for third and fourthyear students, and the mathematical maturity of a senior student will be assumed.
A continuation of C&O 480 (History of Mathematics 1), but may also be taken independently. Topics include: the Fibonacci sequence; prime numbers; Fermat's last theorem; Gaussian integers: Euler's formula and regular solids; famous problems in geometry.
Prereq: MATH 130b, 134a/b (220b, 224b are recommended)
Although the mathematics for this. course is technically elementary, the course is intended for third and fourthyear students, and the mathematical maturity of a senior student will be assumed.
Optimization : Prereq: Consent of department