CO 301 Ancient Myth and Religion 1F 3C 0.5
A study of Greek and Roman myth, including the birth of the gods, creation, the Olympians, Prometheus and the fall, the flood, the ages of man.
Combinatorics and Optimization (CO)
32 courses in the 1982–83 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
Combinatorics and Optimization Course Descriptions
CO 220 Introductory CombinatoricsF,W 3C 0.5
Elementary principles of enumeration. Principles of inciusion - exclusion, generating functions, recurrence equations. Elementary graph theory and graphical algorithms. introduction to design theory.
Prereq: None.
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 Callege in Winter term.
CO 230 Introduction to CombinatoricsF,W,S 3C 0.5
Introduction to the combinatorics of ordinary and exponential generating
‘ functions. Introduction to basic graph
theory and graphical algorithms. Prereq: MATH 134b
Credit will be granted for only one of C&O 220 or C&O 230.
CO 270 Introduction to OptimizationF,W 3C 0.5
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 120b and MATH 1246 C&O 270 is recommended, but not required, for 300-level modelling courses. C&O 350, 367 and 370 are basic courses in optimization and modelling, and may be taken in the
"second term of Year 2.
Also offered by St. Jerome's College in Fall term.
CO 330 Enumeration and DesignF,W 3C 0.5
The combinatorics of ordinary and exponential generating functions. Decompositional methods. The Lagrange theorem. Applications to enumeration of sequences, trees, covers and random waiks. Mutually orthogonal Latin squares and finite projective planes. Symmetric balanced incomplete block designs. Steiner triple systems. Prereq: MATH 224b and C&O 230.
CO 331 Coding TheoryW 3C 0.5
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 by St. Jerome's College.
CO 342 Graph Theory 1F,S 3C 0.5
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 and C&O 230
CO 343 Graph Theory 2W 3C 0.5
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
CO 350 Linear ProgrammingF,W,S 3C 0.5
A first course in problem formulation and solution techniques in linear programming. The simplex and revised simpiex methods. Theory and applications of duality theory. Sensitivity Analysis.
Prereq: MATH 224a
CO 351 Network Flow TheoryF,W 3C 0.5
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. Preregq: C&O 350
CO 367 Mathematical ProgrammingF,W 3C 0.5
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 220a and MATH 224a
CO 370 Deterministic OR ModelsF,S 3C 0.5
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 124b
CO 371 Stochastic OR ModelsW 3C 0.5
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
CO 380 Mathematical Discovery and Invention 1W,S 3C 0.5
A study of about 100 challenging problems taken from many areas of elementary mathematics - number theory, combinatorics, geometry, probability, jogic.
Prereq: None.
CO 381 Mathematical Discovery and invention 2
Not offered 1982-83.
CO 382 Combinatorial GeometryF 2C 0.5
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. Jerame’s College.
CO 430 Algebraic EnumerationF 3C 0.5
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
CO 434 Combinatorial DesignF 2C 0.5
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 324.
Course Descriptions
Mathematics.
Combinatorics and Optimization
CO 438 Combinatorial ComputingW 3C 0.5
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
CO 439 Topics in CombinatoricsW 2C 0.5
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.
CO 440 Topics in Graph TheoryF 2C 0.5
An in-depth study of one or twa 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. Prereg: C&O 342 or consent of instructor. ‘
CO 450 Combinatorial OptimizationW 2C 0.5
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
CO 452 Integer ProgrammingS 2C 0.5
A study of several techniques for solving integer (linear) programming problems. Cutting planes, implicit enumeration, branch-and-bound. Introduction to Boolean and pseudo- Boolean programing. Applications to problems of optimum routing, site location, set covering and packing, lagic and lattice theory.
Prereq: C&O 351
CO 454 SchedulingF,S 30.05
Sequencing algorithms for scheduling tasks on single machines, parallel 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 C&O 370
CO 456 Game TheoryW,S 3C 0.5
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
CO 458 Numerical Linear ProgrammingF 3C O05
Methods for the minimization and maximization of piecewise linear functions and linear functions subject to tinear 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.
N.B: Cross-listed with CS 473.
CO 459 Topics in OptimizationS 2C 0.5
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
CO 464 Quadratic Programming
CO 466 Continuous Optimization.W 2C 0.5
Geometry and numerical algorithms of nonlinear 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 367
CO 480 History of Mathematics 1F 2C 05°
A study of selected topics from Greek geometry. Some related work of postrenaissance scholars is included. Topics
include: 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.
CO 481 History of Mathematics 2W 2C 0.5
A study of selected topics from postrenaissance 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: None.
CO 499 Reading in Combinatorics and OptimizationF,W,S 2R 0.5
Prereq: Consent of department.