MATH 499Readings in Mathematics

1973–74 to 1975–76 3 calendars

2 hours lectures, one term

Professor and Chairman of the Department

Professor, Associate Dean Engineering Graduate Studies

Professor, Associate Chairman Graduate Studies Professor, Associate Dean Engineering Undergraduate Studies

Professor, Associate Chairman Undergraduate

Studies

Professors

Associate Professors

Assistant Professors

• 1973–74 PDF p. 486
• 1974–75 PDF p. 547
• 1975–76 PDF p. 380

1972–73 1 calendar

Another title: Reading in Mathematics Topics in Computer Science, probably a different course under the same number (or a misread scan).

This course will be offered on an experimental basis during the Fall/1972 and Winter/1973 academic terms. Enrolment will normally be restricted to students in fourth year. Topics available will include: 1) Advanced Applications Programming 2) Advanced Systems Programming 3) Systems Analysis 4) Simulation

• 1972–73 PDF p. 449

1969–70 to 1971–72 3 calendars

Titled Reading in Mathematics.

Graduate and Research Programmes

The Faculty offers graduate work over a broad spectrum of the various branches of Mathematics and fields of special interest include: Abstract Algebra, Biometry, Calculus of Variations, Combinatorial Analysis, Computer Science, Control Theory, Differential Equations, Differential Geometry, Foundations, Functional Analysis, Functional Equations, Graph Theory, Harmonic Analysis, Information Theory and Nets, Mathematical Logic, Number Theory, Numerical Analysis, Optimization, Probability, Quantum Theory, Relativity Theory, Statistical Inference, Switching and Automata Theory. The University of Waterloo has at present five computer systems available to Mathematics faculty and graduate students. These are: an IBM System/360 Model 75, and IBM System/360 Model 44, an IBM/360 Model 50, an IBM 1710, an IBM 1620 and peripheral equipment which includes an IBM 2250 Graphic Display and a CALCOMP plotter. The IBM 1620 computer is available to undergraduate students at all times. The IBM 1710 is used by undergraduates, graduates, faculty and staff.. The System/360 Model 75 is run on a closed shop basis but all members of the University can get programmes processed within a reasonably short period of time. The System/360 Model 44 is used in process control applications and provides the University with a centralized process control facility. The System 360 Model 50 is used by undergraduates, graduates and faculty for development of software in Computer Science as well as a facility for handling the conversational language APL. Extensive financial assistance is available through National Research Council Scholarships and Bursaries and Province of Ontario Graduate Fellowships. In addition, the Faculty of Mathematics offers a number of Teaching Fellowships and some Research Assistantships. For details, correspondence should be addressed to the Graduate Office of the Faculty or Department Chairmen. Candidates for the degrees of M.Math., M.Phil. and Ph.D. are accepted under the general regulations set forth in the section of the

Applied Analysis and Computer Science

Applied Mathematics

Faculty of Mathematics 357

M.Math. degree are encouraged to present theses. Those proceeding by course work must submit a substantial essay in addition to their programme of courses.

Faculty members of the Department of Applied Analysis and Computer Science are currently engaged in a varied and extensive research programme including: i

Programming: Software developed at the University of Waterloo is currently being used by Computing Centres throughout the world. In particular, its well-known WATFOR and WATFIV compilers are currently being used by over 350 System/360 installations. Several installations are using a similar compiler developed in 1965 for 7040-7044 Series machines. Many other topics are being studied including coroutine systems, symbol manipulation, and design of programming languages, both general purpose and also with particular emphasis on software implementation.

Machine Organization and Fault Diagnosis: Current research includes the development of software aids to fault diagnosis, the investigation of unorthodox machine organization from the viewpoints of fault diagnosis and system availability, and the self-diagnosis problem for digital processors. Also under study are system problems arising from time sharing such as the problem of testing software, and computer networks. Computer-Aided Design: The improvement of design techniques through the use of digital computers and associated devices such as visual display units is presently under study.

Formal Languages, Automata and Switching Theory: Among the problems being investigated are the algebraic theory of languages and structure theory of sequential machines.

Computability Theory: Topics currently being studied are Turing machines, complexity classifications of computable functions, abstract models of digital computers and hierarchies of classes of recursive functions.

Artificial Intelligence: One of the problems presently being studied is computer-assisted theorem proving.

Numerical Analysis: Algorithms for two-point boundary problems, stiff systems of differential equations, atomic structure equations, unilateral matrix equations, optimization problems, and linear algebra techniques are presently under investigation.

Functional Equations: Besides basic research, the fields investigated include fundamental applications in nomography, information theory, theory of complex variables, algebraic structures, geometry and generalized functions in general spaces.

Combinatorics and Optimization, Mathematical Operations Research, Graph Theory, Statistics and Decision Theory: Research in these areas is being conducted by members of other departments in the Faculty of Mathematics.

Research in the department is being carried out in a number of areas related either directly or indirectly to problems in Mathematical Physics. These areas include Linear and Nonlinear Differential Equations, Special Theory of Differential Operators, Optimal Control Theory, Boundary Layer Problems in Fluid Dynamics and Particle Physics. A Relativity group is being formed within the department with interests in General Relativity, Differential Geometry and the Calculus of Variations. The department also has a very active Quantum Theory Group whose research involves the Quantum Theory of Crystals and Surfaces.

Combinatorics and Optimization

Pure Mathematics

Statistics

Faculty of Mathematics

The department sponsors a number of seminars, invited talks by outstanding people in the various fields and visiting Professors. Graduate students are encouraged to become involved in these programmes.

Research currently being pursued in the Department of Combinatorics and Optimization includes work in graph theory, chromatic polynomials, colouring problems and enumeration, design theory, matroid theory, well-quasi-ordered sets, directed graphs and relations, Boolean algebra and its applications to Optimization, applications of linear programming and convex polyhedra to Combinatorics and Optimization, extremal problems in graphs, minimax theorems, algorithms and computer analysis in Combinatorics and Optimization, theory of formal languages, and mathematics of elementary particle physics. Research and teaching in Optimization emphasize the underlying mathematical theory, and especially applications of Combinatorics. The department is developing a computerized reference retrieval system for graph theory, which may be extended to cover other areas of Combinatorics and Optimization.

The following graduate courses are offered by the Department of Combinatorics and Optimization: 780, 782, 785, 788, 789, 791, 792, 793, 798, 969, 971, 973, 981, 982.

There are several research activities in the department. These include work in Geometry (Foundations of Geometry, Combinatorial Geometry, Special Geometries including Geometries over Algebras and Finite Geometries, Topology), work in Algebraic Structures (General Algebraic Systems, Linear Algebra, Lattice Theory, Group Theory) and work in Logic and Foundations, moreover some aspects of Analysis and Number Theory.

The departments of Philosophy and Pure Mathematics have inaugurated a joint graduate programme for students interested in the foundations of mathematics and related problems.

There is a weekly meeting of a Research Seminar on “Geometrical and Algebraical Structures”, where original mathematical investigations by students and professors are presented.

Research in the Department of Statistics centres on the controversial problem of formulating exact statistical inferences in many diverse situations using generalizations of the approach introduced by the late Sir Ronald Fisher in his foundation of the theory of fiducial inference, the theory of the likelihood function and the theory of estimation in general. The extensive computing facilities available at the University of Waterloo have given rise to investigations into the uses of computers to obtain exact results on the basis of these theories in situations previously treated by asymptotic methods, and also research into exact tests in multivariate analysis.

Related to this research, there is active interest in problems of experimental design, with particular reference to incomplete block designs, multivariate analysis, estimation theory, mathematical genetics and stochastic processes as applied, for example, to biometrical problems, such as the analysis of environmental factors contributing to diseases processes and aging.

Members of the department are also interested in problems in combinatorial mathematics, such as the construction of balanced incomplete block designs, which arise in the design of experiments. Other combinatorial questions under consideration include edge-chromate graphs and the Ramsey numbers.

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Faculty of Mathematics 359

Increasing contact with the Department of Psychology and with work in the Physical Sciences, undertaken as part of the above-mentioned biometrical studies, provides a variety of new problems and also gives advanced students a valuable opportunity to apply lecture material to useful practical situations. An arrangement with the Statistics Unit of the Department of Agriculture in Ottawa provides potential summer employment for advanced undergraduates and at the same time, a further opportunity for practical experience.

Courses

An asterisk (*) indicates courses given in 1970-1971 academic year. Other graduate courses may be given from time to time as demand warrants.

Survey of Algebra and its Applications.* Survey of Numerical Analysis. Computer Programming.* Mathematical Logic.*

Transfinite Arithmetic.

Axiomatic Set Theory.

Recursive Function Theory.* Algebraic Theory of Numbers. Seminar in Logic and Foundations.* Seminar in Number Theory.* Topics in Logic and Foundations.* Topics in Number Theory. Universal Algebra.*

Groupoids and Quasigroups. Infinite Groups.

Representation Theory. Homological Algebra.

Seminar in Group Theory.

Topics on General Algebraic Systems.* Topics in Group Theory.

Rings and Ideals*.

Multilinear Algebra.*

Galois Theory.

Topics on Rings and Fields. Differential Geometry.

Differential Manifolds.

Topological and Lie Groups. Algebraic Topology.*

Seminar in Homotopy Theory.* Special Topics in Geometry.* Topics in Topological Structures.* Combinatorial Analysis* Combinatorial Graph Theory.* Analytic Graph Theory.

Linear Graphs.

Planar Graphs.

Extrema in Graphs.

Directed Graphs.* Combinatorics.*

Matroid Theory.*

Boolean Methods in Combinatorics and Optimization.*

813 815 817 819 820 828 829 830 832 834 835 836 837 848 849 850 851 852 855 858 859 860 861 862 864 865 867 869 870 871 872 873 876 878 879 881 885 886 890 891 892 893 894 895

897 898 899 900 902

one

Faculty of Mathematics

Seminar in Graph Theory.

Topics in Graph Theory.

Seminar in Combinatorial Analysis.*

Topics in Combinatorial Analysis.

Harmonic Analysis.

Orthogonal Series.

Functions of a Complex Variable (Analytic Function Theory) Special Functions.

Abstract Measure Theory.*

Functional Analysis.

Linear Operators.

Topics in Classical Analysis.

Topics in Functional Analysis.*

Potential Theory.

Ordinary Differential Equations.* Introduction to Partial Differential Equations. Hyperbolic Partial Differential Equations. Elliptic Partial Differential Equations. Parabolic Partial Differential Equations. Topics in Potential Theory.

Topics in Differential Equations.

Functional Equations for Functions of One Variable.* Functional Equations in Several Variables. Functional Equations for Analytic Functions. Integral Equations.

Seminar on Functional Equations.*

Topics on Functional Equations.

Calculus of Variations.

Analytic Theory of Geometric Objects. Vector and Tensor Analysis.

Integral Transforms.*

Calculus of Operators.

Theory of Approximation.

Survey of Numerical Analysis.

Numerical Solution of Ordinary Differential Equations.* Numerical Methods in Linear Algebra.* Numerical Solutions of Partial Differential Equations.* Problems in Numerical Integration.

Seminar in Numerical Analysis.*

Topics in Applied Analysis.

Topics in Numerical Analysis.

Introduction to Switching and Automata Theory.* Time-Sharing Systems.*

Computer Systems.*

Computer Programming.*

The Theory and Construction of Compilers.* Data Structures | and 2.*

Data Structures 3.*

Finite Automata.*

Design of Sequential Machines.

Algebraic Structure of Sequential Machines. Formal Languages.*

Computability Theory.*

Statistical Information Theory.

Measurement of Information.

Artificial Intelligence.*

Baminne to Dawes O-5-- ++

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961

965 966 967 969 970 971 972 973 975 976 978 979 981

992

995 996

M690 M692 M693 M694 M695 M696 M697 M699

Faculty of Mathematics

Fault Diagnosis of Digital Systems. Topics in Information Theory. Introduction to Random Variables. Theory of Probability.*

Stochastic Processes.*

Seminar in Probability Theory.

Topics in Probability Theory.* Mathematical Genetics.

Topics in Probability and Biometry. Topics in Biometrical Statistics.* Foundations of Statistics.*

Estimation and Hypothesis Testing.* Advanced Statistics.*

Applied Statistics.*

Seminar in Statistics.

Topics in Statistics.

Complex Variable Techniques in Physical Problems. Group Theory in Physical Problems. Continuum Mechanics.

Fluid Mechanics.

Mathematical Electrodynamics. Quantum Molecular Physics.* Quantum Mechanics.

Elementary Particles.

Mathematical Theory of Relativity.* Statistical Mechanics.

Quantum Surface Physics.*

Control Theory.*

Quantum Crystal Physics.

Topics in Applied Mathematics. Mathematical Optimization.

Directed Graphs and Applications.* Mathematical Programming.* Network Programming.

Mathematical Operations Research. Seminar in Mathematical Operations Research Seminar in Combinatorics and Optimization.* Topics in Optimization.

Game Theory.*

Data Processing for Behavioural Scientists. Mathematical Methods for Science and Engineering.* Numerical Methods and Programming. Seminar in Mathematics Education. Topics in Mathematical Education. Topics in the History of Mathematics. Literature and Research Studies. M.Phil. Comprehensive Examination Ph.D. Comprehensive Examination Language Requirement

M.Math. Essay

M.Math. Thesis

M.Phil. Thesis

Ph.D. Thesis

Note

• 1969–70 PDF p. 271
• 1970–71 PDF p. 333
• 1971–72 PDF p. 365