26 courses in the 1981–82 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions
Note
Course descriptions are given under the new course numbers introduced in 1980. The old numbers appear in brackets.
Cc & O 220 F,W 3C 0.5 Introductory Combinatorics Elementary principles of enumeration. Principles of inclusion - exctusion, generating functions, recurrence equations. Elementary graph theory and graphical algorithms. Introduction to design theory. Prereq: None
N.B.; Credit will be granted for only one of C & O 220 or C & O 230. C & O 220 cannot be counted for credit toward a BMath Honours degree. Offered by St. Jerome’s College in Winter Term.
(C & O 280)
Introduction to the combinatorics of ordinary and exponential generating functions. Introduction to basic graph theory and graphical algorithms. Introduction to coding theory.
Prereq: Math 134a/b
N.B.: Credit will be granted for only one of C & O 220 © or C & O 230.
(C & O 282)
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 220a and Math 224a (or Math 221a/b) Also offered by St. Jerome’s College in Fall Term.
The combinatorics of ordinary and exponential generating functions. Decompositional methods. The Lagrange theorem. Applications to enumeration of sequences, trees, covers and random walks. Mutually orthogonal Latin squares and finite projective planes. Symmetric balanced incomplete block designs. Steiner triple systems.
Prereq: Math 224b (or Math 321a)
A first course in error correcting codes. Linear block codes, Hamming-Golay codes and multiple errorcorrecting BCH codes are studied. Various encoding and decoding schemes are considered. | Prereq: Math 224b (or Math 321a)
Offered by St. Jerome’s College.
An introduction to the ideas, methods and applications of graph theory. Finding shortest paths and maximum matchings in weighted graphs. Determining the connectivity of a graph.
Prereq: Math 224a (or Math 221a/b)
(C & O 370a)
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. Theory and applications of duality theory. Sensitivity Analysis.
Prereq: Math 224a (or Math 221a/b)
(C & O 331a)
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
(C & O 331b).
Review of linear programming via the projection method. Parametric linear programming. Introduction to optimality conditions and duality for nonlinear optimization. Overview of some nonlinear programming algorithms.
Prereq: Math 220b and Math 224a (or Math 221a/b)
5 (C & O 433a)
Cc & O 370 F,S 3C 0.5 Deterministic OR Models
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: Math 224a (or Math 221a/b)
(C & © 340)
Combinatorics and Optimization .
'
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
(C & O 384) Mathematical Discovery and Invention 1
A study of about 100 challenging problems taken from many areas of elementary mathematics - number theory, combinatorics, geometry, probability, logic.
Prereq: None
Cc &0 381 W 2c 0.5 (C & O 385) Mathematical Discovery and Invention 2
A study of about 100 challenging problems taken from many areas of elementary mathematics - number theory, combinatorics, geometry, probability, logic.
Prereq: None
Combinatorial aspects of the plane. The number of regions determined by various geometrical curves. Pick’s theorem, Sylvester’s triad problem, squaring the rectangle, convex sets and finite geometry. Prereq: None
Offered at St. Jerome’s College.
(C & O 386a)
Cc & O 430 F 3C 0.5 Algebraic Enumeration
The course is an extension of C & O 330. The combinatorics of Eulerian generating functions, the algebra of sequence types, maximal decomposition theorem. Lagrangian methods and their applications. Random walks and the Hopf factorization. Symmetric functions and plane partitions.
Prereq: C & O 330
(C & O 460)
This is a continuation of C & O 330. Topics covered include error correcting codes, resolvable designs, affine designs, weighing matrices, and their interaction.
Prereq: C & O 330 and Math 324a (or Math 331b)
(C & O 462)
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 330 and C & O 342 are recommended.
(C & O 464a)
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.
Prereq: Consent of instructor.
(C & O 470b)
An in-depth study of one or two 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, probabalistic graph theory, connectivity, graph embedding, colouring problems. Prereq: C & O 342 or consent of instructor.
(C & O 470a)
Packing, covering and partitioning problems. 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
(C & O 431a)
C&0O0452 °9W 2C 0.5 Integer Programming
A study of several techniques for solving integer (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
(C & O 436)
Course Descriptions Combinatorics and Optimization
Sequencing algorithms for scheduling tasks on single machines, parallel machines, and flow shops. Applications to scheduling computers and manufacturing facilities. Combinatorial techniqués used in algorithm development and convergence proofs.
Prereq: C & O 351 or C & 0370
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
(C & © 442a)
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 370, or consent of instructor.
(C & O 433b)
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 optimiality 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 367
(C & 0,443b)
Geometry and numerical algorithms of nonlinear optimization. Variable metric and conjugate gradient methods. Convex programming. Feasible and nonfeasible direction methods. Recursive quadratic programming, non-orthogonal projections and active set strategies.
Prereq: C & O 367
(C & O 432)
A study of selected topics from Greek geometry. Some related work of post-renaissance scholars is included. Topics inctude: famous construction problems, pythagorean arithmetic, regular solids, four discoveries of Archimedes, the problem of Apollonius; selected works of Archimedes, Euclid, Apollonius, Euler, Steiner.
Prereq: None
(C & O 487)
A study of selected topics from post-renaissance mathematics. Topics include material on prime numbers, Fermat's Last Theorem, the Gaussian Integers, the Fibonacci Sequence, other topics from elementary number theory, a collection of outstanding problems in geometry (Fagnano, Steiner- Lemus, Morley).
Prereq: Noné
(C & O 488)
Prereq: Consent of department