MATH 610 Quantitative Simulations (a) Introduction to Modelling
(b) Socioeconomic Systems.
Mathematics (MATH)
160 courses in the 1968–69 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
(a) Vector Algebra to Linear Programming; Variational Methods to Dynamic Programming.
(b) Statistical Decision Theory; Stochastic Processes.
MATH 615 Management Decision-Making Laboratory
Participation in analysis, planning, and decision-making under competitive and fast-time stress using functional and industrial simulations.
618* and 619* People, Machines and Organizations. Interpersonal and group behaviour in systems of people and machines; phenomena of perception, communication, learning, decision-making, morale, conflict resolution, and goal-seeking. Problems in perceiving and modelling behaviour; the human factor in organization design.
Function-oriented Courses
620.* Introduction to Marketing. Techniques in market research, product, and market analysis; modelling of consumer and industrial market behaviour; competitive strategy in marketing planning; distribution systems design; sales forecasting. Economics of information sampling and consumer surveys.
630.* Introduction to Production. Techniques of production planning and control; models of aggregate production and workforce, interaction of production and inventory control; scheduling algorithms.
632.* Operations Research in Processing Industries. Systems representation of single and multi-unit processing facilities, experiment design to measure system parameters; simulations including economic factors; sensitivity analysis, production planning and control; capital resource evaluation; process optimisation.
640.* and 642* Strategies of Research and Development. Review of factors influencing the effect of research and design on a business or national economy. Economic measurement; information flow; organization theory; psychology of discovery and innovation. Case histories of technological changes.
650.* Introduction to Information Processing. The nature of information as a product of complex systems; element and rule concepts; decision tables; document tracing; report generation; communication networks; data banks; decision-organization and work flow relationships; generalized study of the creation of an information system; nature and role of EDP in an information system; information retrieval.
652.* Advanced Information Processing. The nature of a system; system elements and relationships; structuring a business system; management objectives, organizational
concepts; the information system; organizing a data processing centre; task force se-
Management and Systems Engineering Programme
lection and training, hardware selection; satellite computer systems; tele-processing; data linkages and sub-systems; the total system concept.
660.* Introduction to Corporate Finance. Capital Sources; investment psychology, strategic and probabilistic considerations in financial planning.
662.* Advanced Corporate Finance.
665.* Introduction to Corporate Law. Legal concepts as expressed in laws pertaining to company organizations, contracts, securities, and patents. Court administration and procedure. Information retrieval and O.R. applications in legal and legislative procedures.
Advanced Methodology (Advanced Graduates)
680.* Advanced Stochastic models. Properties and characteristics of stochastic models, with emphasis on Markov and Poisson process, queuing theory models and applications.
682.* Network Methods. Advanced network methods, with maximal flow algorithms, as related to production control, plant location.
684.* Advanced Mathematical Programming. Review of non-linear, quadratic, and integer programming, also convex programming. Extension of linear programming with possibly non-linear objective functions and constraints; and integer solutions.
686.* Quantitative Economics and Econometrics. Local, regional and national economic planning for developing and industrial economies, using quantitative models.
Advanced Integrative Courses (Advanced Graduates)
MATH 690 Corporate Planning
Modelling as an approach to problem identification and solution in corporate planning: organization, capital budgetting, forecasting. Case studies in corporate development, dynamics of growth and contraction, strategic decision making.
(2 terms).
692.* Public Sector Management. Operations and systems analysis in public adminis-
tration: police, health services, education, monetary and fiscal control, defense, public works. Case studies in governmental and institutional decision-making.
695.* Evaluation of Current Research. Seminar: review of current literature in Operations Research, Systems, Management Science, etc.
791, 792. Project.
MATH 809 Thesis for the Ph.D
Areas of Special and Continuing Interest
Technological Innovation and Creativity. Information flow, technological history and the satisfaction of demand and supply constraints; human, organisational, and physical factors under control of management; social, legal and economic environmental influences.
Operational Information Systems. Application of computerised information-processing methodology to mechanisation and control of mixed man/machine operations as in marketing, production, accounting, project management; diagnosis of faulty systems.
Simulations, Models, Optimal Decision-making. Development and refinement of mathematical models of systems, and subsystems; application of quantitative and probabilistic methods to decision-making, prediction, and control.
Enterprise and Competitive Strategies. Venture planning and analysis; patent management; financial planning and strategy in growth situations; capital growth optimization; game theory applications; decision-making under competitiv> stress; optimal resource allocation in public and private operational environment.
Social Science Applications in Management. Interaction between humans, and between
humans and machines, in organisations; behavioural patterns and purposes; learning and motivation; perception and decision-making in competition and co-operation.
Faculty of Mathematics
Faculty of Mathematics
Department of Applied Analysis and Computer Science
D. D. Cowan, B.A.Sc. (Toronto), Ph.D. (Waterloo) Associate Professor Chairman of the Department
J. Aczel, Ph.D. (Budapest), Habil. D.Sc. (Hung. Ac. of Science) Professor J.A. Brzozowski, M.A.Sc. (Toronto), Ph.D. (Princeton) Professor J.W. Graham, M.A. (Toronto} Professor and Director of Computing Centre H. Haruki, Ph.D. (Osaka) Professor M.A. McKiernan, M.A. (Loyola), Ph.D. (Illinois Institute of Technology) Professor J.D. Lawson, B.A.Sc. {Toronto}, Ph.D. (Waterloo) Associate Professor P. C. Jennings, B.A. (Utah), Ph. D. (Texas) Assistant Professor (Psychology and Mathematics)
R. B. Roden, M.A. (Toronto), Ph. D. (Cambridge) Assistant Professor (Computing Centre and Mathematics}
J.C. Wilson, B.A.Sc. (Toronto), Ph.D. (Waterloo) Assistant Professor J.H. Vellinga, B.A. (Western), M.A. (Waterloo) Assistant Professor (Part-time) P. Brillinger, B.Sc. (McMaster), M.A. (Waterloo) Lecturer R.S. Cohen (Mrs.), M.Sc. (Technion-Haifa) Lecturer P.H. Cress, B.Sc. (Toronto), M.Sc. (Waterloo) Lecturer P.H. Dirksen, M.Sc. (Waterloo) Lecturer B.O. Nash, B.Sc. (Tilinois), M.A. (Waterloo) Lecturer C.R. Zarnke, M.A. (Waterloo) Lecturer
B.L. Ehle, B.A. (Whitman College), M.S. (Stanford) Lecturer { Part-time)
Lecture in Faculty of Mathematics
Department of Applied Mathematies
P. J. Ponzo, M.A. {Toronto}, Ph. D. {Illinois} Associate Professor Chairman of the Department H.F. Davis, Ph.D. { Massachusetts Institute of Technology)
(On Sabbatical Leave 1967-1968) Professor C.F.A. Beaumont, B.A. (McMaster), M.A. {Toronto} Associate Professor and Associate Dean of the Faculty of Mathematics
J. Froese, B.A. (Manitoba), M.A. (Queen's), Ph.D. {British Columbia) Assistant Professor
G.J. Lastman, M.A. (British Columbia), Ph.D. {Texas) Assistant Professor IJ. McGee, B.A.Sc. {Toronto}, M.Sc. (Waterloo), Ph.D. (Yale) Assistant Professor M.E. Snyder (Mrs.), B.Sc. (Western), M.A.Sc. (Waterloo) Assistant Professor
J. Wainwright, B.Sc. (Univ. of Natal), Ph.D. (Univ. of South Africa) Assistant Professor
R.A. Wentzell, B.Sc. (Acadia), Ph.D. (Western) Assistant Professor V.M. Bobetic, M.A. (Univ: of Zagreb, Yugoslavia) Lecturer F. Burkowski, M.Sc. (Waterloo) Lecturer D.I. MacLeod, M.A. (Waterloo) Lecturer D.W. Trim, M.Sc. (Waterloo) Lecturer B. Wilkinson (Miss), M.Sc. (Waterloo) Lecturer
Department of Combinatorics and Optimization
G. Berman, Ph.D. {Toronto} Professor and Chairman of the Department C. Nash-Williams, Ph.D. (Cambridge) Professor W.T. Tutte, Ph.D. (Cambridge) F.R.S.C. Professor R.C. Mullin, B.A. (Western), Ph.D. (Waterloo) Associate Professor R.A. Honsberger, B.A. (Toronto), M.A. (Waterloo) Assistant Professor
U.S.R. Murty, M.A. (Osmania), Ph.D. (Indian Statistical Institute) Assistant Professor
R.N. Burns, B.Sc. (Toronto), M.A. {Waterloo) Lecturer J.W. Dodd, B.A.Sc. {Toronto}, M.Sc. (Waterloo) Lecturer R.G. Dunkley, B.A. (Western) Lecturer {Part-time} and Assistant to the Dean G.B. Faulkner, B.Sc. (Toronto), M.Sc. (Waterloo) Lecturer C.E. Haff, B.S. (Stanford) Lecturer W.I. Miller, B.A. (Queen's) Lecturer {Part-time} and Assistant to the Dean A. Morofke, M.Sc. (Waterloo) Lecturer G.N. Robertson, M.Sc. (Manitoba) Lecturer
Department of Pure Mathematics
D.G. Wertheim, B.A. (McMaster), Ph.D. (Toronto) Professor Chairman of the Department
G.E, Cross, M.A. (Dalhousie), Ph.D. (British Columbia) Professor Dean of Graduate Studies
K.D. Fryer, B.A. (Western), Ph.D. (Toronto) Professor
Associate Dean of the Faculty of Mathematics
Faculty of Mathematics
H.H. Crapo, A.B. (Michigan), Ph.D. {Massachusetts Institute of Technology) Associate Professor A. Kerr-Lawson, B.A. (Toronto), S.M. (Chicago), Ph.D. (McMaster) (On Sabbatical Leave 1967-1968) Associate Professor R.A. Staal, Ph.D. (Toronto) Associate Professor F.C.Y. Tang, B.Sc. (Hong Kong), M.S. (South Carolina), Ph.D. (Illinois) Associate Professor Paul de Witte, 4.Sc. Theor.Phys. (Ghent), M.Sc. Math. ( Brussels), Ph.D. (Brussels). Associate Professor of Foundation of Mathematics E.R. Bishop, B.Sc. (Acadia), M.Sc. (Queen’s), Ph.D. (McMaster) Assistant Professor L.J. Cummings, B.S. (Roosevelt Univ.), M.S. (DePaul Univ.}, Ph.D.
(British Columbia} Assistant Professor D. Higgs, B.Sc. Hons. {Rand}, M.A. (Cantab.} Assistant Professor P. Hoffman, B.A. (Toronto), Ph.D. {Manchester) Assistant Professor D.J. Miller, PA. D. (McMaster) Assistant Professor E.M. Moskal, B.A. (Toronto), Ph.D. (Illinois) Assistant Professor K.A. Rowe, B.A. (Toronto), M.S. (Wisconsin), Ph.D. (Illinois) Assistant Professor S. Aczel (Mrs.), M.A. (Szeged) Assistant Professor ( Part-time} M. Johnson, M. Math. (Waterloo) Lecturer R. Kingsley, M@. Math. (Waterloo) Lecturer J. Malzan, M.A. (Toronto) Lecturer B.S. Thomson, B.Sc. (Toronto), M.Sc. {Waterloo) Lecturer J.K. Vranch, M.Sc. {Waterloo} Lecturer R.C. Wilton, M. Math. (Waterloo) Lecturer
Department of Statistics
D.A. Sprott, Ph.D. (Toronto) Professor Chairman of the Department and Dean of the Faculty of Mathematics
W.F. Forbes, D.LC., Ph.D., D.Sc. (London) Professor (Chemistry and Mathematics)
J.S. Minas, B.A. (Wayne), Ph.D. (Illinois) Professor (Philosophy and Mathematics} and Dean of the Faculty of Arts
G.W. Bennett, Ph.D. (Adelaide) Associate Professor M.D. Vogel-Sprott, (McMaster), Ph.D. (Toronto) Associate Professor (Psychology and Mathematics)
J.G. Kalbfleisch, B.Sc. (Toronto), Ph.D. (Waterloo) Assistant Professor
R.V, Thysell, B.S. (Montana), Ph.D. (State University of lowa) Assistant Professor (Psychology and Mathematics)
E. Haag, B.Sc. (Queen’s) M.A. (Waterloo) Lecturer J.S. Huang, B.A. (Taiwan Univ.}, M.B.A. {Univ. of Georgia) Lecturer J.D. Kalbfleisch, M. Math. (Waterloo) Lecturer J.F. Lawless, M.Sc. (Waterloo) Lecturer A.C. Madgett, B.Sc. (Toronto), M. Phil. (Waterloo} Lecturer C. Springer, M.Sc. (McGill) Lecturer V. Taht, M.A. (Toronto) Lecturer M.R. Wise, 8. Math. {Waterloo} Lecturer
D.B. Martin, B. Commerce (Manitoba), Associate of Society of Actuaries Adjunct Professor
P.Robinson, Dip. Math. Stat. (Cambridge), Ph.D. {University of Cape Town} Adjunct Professor
Visiting Professors
G. Alexitis, Ph.D. (Graz. Austria) Professor W. Benz, Ph.D., Habil. (Mainz) Professor E. Berz, Ph.D., (University of Munich}, Venia Legendi, (University of Giessen) Professor E.T. Davies, M.Sc. (Wales), Dottore in Matematica (Rome) Professor Ph. D., D. Sc. (London University) I. Fenyo, Ph.D., Habil. (Budapest) Professor V.P. Godambe, M.Sc. (University of Bombay), Ph.D. (University of London} Professor L. Kalmar, Ph.D., D.Sc. (Budapest) Professor R.S. Mishra, Ph.D. (University of Delhi, India), D.Sc. (Lucknow University) Professor A. Ostrowski, Ph.D. (Gottingen), Dr. Math. h.c. ETH Ziirich Professor G.P. Patil, Ph.D. (University of Michigan) Professor T. Pietrzykowski, M.A. (University of Warsaw), Ph.D. (Polish Academy of Science} Professor
W. Eichhorn, Dipl. Math., Dipl. Volksw., Dr. rer. nat., D. Habil. (Wurzburg) Associate Professor P.K. Kamthan, M.Sc. (Lucknow), Ph.D. (Rajasthan) Associate Professor P.L. Kannappan, M.A. (Annamalai), Ph.D. (University of Washington) Associate Professor
M.E. Watkins, Ph.D. (Yale) Associate Professor D. Younger, Ph.D. (Columbia) Associate Professor D.Z. Djokovie, Ph.D. (Belgrade) Research Associate Professor
Undergraduate Course Descriptions
Note The number of hours or lectures shown after the course description is an attempt to indicate the “‘normal’’; each instructor determines how often his particular class will meet.
MATH 12 Calculus I
Functions and limits, the derivative. Differentation formulae. Applications to tangents, rates, extremes. The indefinite and definite integrals, fundamental theorem of integral calculus. Applications to area, volume, centroids, moments of inertia, fluid pressure, work, potential. Introduction to the trigonometric, inverse trigonometric, exponential, logarithmic functions. Transcendental functions. Parametric and polar equations. Formal! integration and applications to physical problems. Students will work selected problems under supervision. A certain proportion of the problems will include mathematical formulation of physical problems.
2 hours lectures, 3 hours laboratory.
MATH 21 Algebra and Solid Geometry
The rational, real, and complex number systems. Polynomial functions. Theory of equations. Determinants. Vector and matric notation. Co-ordinates in three dimensions. Systems of planes and lines. Standard equations of quadric surfaces. Spherical and cylindrical co-ordinates.
2 hours lectures.
Faculty of Mathematics
MATH 22 Calculus Il
A continuation of course 12. Infinite series and power series. Partial derivatives. Multiple integration and application to areas, volumes, centroids, moments. Introduction to differential equations.
Prerequisite: Math 12. 3 lectures, one term.
MATH 23 Numerical Methods
Introduction to the use of desk calculators. Simple problems on interpolation, solution of algebraic equations, numerical evaluation of intergrals, systems of equations.
1 lecture, 2 hours problems, one term.
MATH 24 Mathematics Problems
A problem course to accompany Math 22. 2 hours problems, one term.
MATH 31 Differential Equations
Standard methods of solution. Applications to physical and engineering problems. Linear equations with constant coefficients. Systems of differential equations. Solution by series. Numerical methods of solution. Partial differential equations; applications of partial differential equations.
Prerequisite: Math 22.
3 lectures, one term.
MATH 32 Numerical Analysis
Ordinary, divided, and central difference interpolation formulae. Graphic and numerical solutions of algebraic and transcendental equations. Computation with series and integrals. Systems of linear equations. Determinants and matrices. Eigenvalue problems. Iterative procedures. Relaxation methods. Difference equations. Mathematical principles associated with electronic computers.
Prerequisite: Math 23.
2 lectures, 2 hours problems, one term.
MATH 33 Differential Calculus
Real numbers, sequences, limits, continuity. The derivative. General Theorem of Mean Value. Functions of several variables. Implicit functions, Jacobians. Power series with complex terms, the Taylor series for functions of several variables, constrained extrema. The elementary functions for a complex variable. Prerequisites: Math 22, 31.
3 lectures, one term.
34, Integral Calculus. Systematic treatment of formal integration. Differential equations. Calculus of variations. Fourier series. Riemann integration, improper integrals, multiple integrals with applications. Line integrals, theorems of Green and Stokes. Prerequisites: Math. 21, 31.
3 lectures, one term.
MATH 41 Applied Analysis I
Partial differentiation, Laplace transforms, special functions.
Fourier series, second order differential equations. 3 lectures, one term.
MATH 42 Vector Methods
Scalar and vector products; curl, divergence, and gradient. Use of vectors and matrices in discussion of physical problems in mechanics, fluid flow, and electromagnetism. Introduction to tensors.
Prerequisites: Math 22, 31, and consent of instructor.
2 lectures, | hour problems, one term.
MATH 44 Complex Variable
Cauchy-Riemann equations, the Cauchy integral theorems, conformal mapping, the Taylor and Laurent series, contour integration. 2 lectures, | hour problems, one term.
MATH 100 Fundamental Concepts of Mathematics
A mathematics course in the liberal arts tradition. A selection of mathematical topics in a context of history, philosophy and applications, The growth of the number system: rational, real, complex, hyper-complex and infinite numbers, vectors and matrices; paradoxes and applications. The limit concept, including an introduction to Calculus: Newton and the influence of Newtonian physics. Abstraction, symbolic logic.and recent trends in mathematics education. Little is assumed in the way of previous knowledge, but the student should have some affinity for mathematics. The course is library-oriented rather than textbook-oriented and the student is encouraged to find and pursue some interest of his own, subject to approval.
3 lectures.
MATH 130 Calculus
Functions and limits. The derivative. Differentiation of algebraic functions. Applications to tangents, rates, minima and maxima. Integration as the limit of a sum. Fundamental theorem of integral calculus with applications to areas, volumes, and moments. Power series. Partial differentiation.
3 lectures.
MATH 131 Algebra and Solid Geometry
The real and complex number systems. Polynomial functions. Theory of equations. Determinants. Vector and matrix notation. Elementary solid geometry, planes and lines, the standard quadric surfaces. Co-ordinate systems.
2 lectures, one hour problems.
MATH 132 Introduction to Computer Science
A thorough introduction to algorithms, stored-programme computers and programming languages. Concept and properties of an algorithm, language and notation for describing algorithms. Analysis of computational problems and development of algorithms for their solution. A procedure-oriented language (FORTRAN IV) and machine and assembly languages are used to implement algorithms on the computer.
2 hours lectures, 2 hours problems.
MATH 140 Calculus
The topics of Mathematics 130, presented with a view to the special needs of Social Science students. Emphasis will be on basic concepts rather than on the more difficult manipulative techniques.
3 lectures.
MATH 229 Linear Algebra
Vector spaces, matrices, groups of transformations. 3 hours lectures.
Faculty of Mathematics
MATH 231 Differential Calculus
Real numbers, sequences. Limits. Continuity. Derivatives. Functions of several variables. Implicit functions. Jacobians. Taylor’s series with geometric applications. Power series with complex terms. The elementary functions for a complex variable.
2 lectures.
MATH 232 Integral Calculus
Methods of formal integration. Differential equations. Fourier series. Riemann integration and applications. Calculus of variations. Line integrals. Stokes’ and Green’s theorems.
3 lectures.
MATH 233 Probability and Statistics
Frequency distributions. Probability. Binomial. Normal, and Poisson laws. Sampling theory. Curve fitting. Distributions of Chi-squared, F, and t. Hypothesis testing. Quality control. Regression theory. Analysis of variance. Introduction to experimental design.
2 lectures, 1 hour problems.
MATH 234 (a) Mechanics 1
Vector Analysis in orthogonal curvilinear co-ordinates, gradient, divergence, curl. Equations of oscillatory systems. Central forces. Rotation and translation of co-ordinate systems and accelerated reference frames.
2 hours lectures, Fall term.
(b) Differential Equations I. Solution of differential equations in series, including Bessel’s and Legendre’s equation. Systems of differential equations. Existence theorem of Picard. Applications to problems in the Physical Sciences.
2 hours lectures, Winter term.
MATH 235 (a) Actuarial Mathematics
Mathematics of Investment: The theory of rates of interest and discount, annuities and sinking funds; application to financial problems, including the determination of mortgage payments and the price and yield of bonds.
2 hours lectures, Fall term.
(b) Basic Life Insurance Mathematics: Applications of probability to problems of life and death. The determination of single and annual premiums for assurances and annuities. Reserves. Company expenses and their incorporation into premium and cash value calculations.
2 hours lectures, Winter term.
MATH 236 Elementary Differential Equations
An introduction to first order differential equations. Applications to growth, decay, reactions. Linear equations with constant coefficients. Systems of equations; vector and matric methods. Solutions in series. Introduction to partial differential equations.
2 lectures.
MATH 237 Differential and Integral Calculus
Real numbers, sequences, limits, continuity, derivatives. Functions of several variables, implicit, functions, Jacobians, Taylor’s series. Methods of formal integration; differential equations. Fourier series, Riemann integration; line integrals.
3 lectures.
MATH 238 Applications in Computer Science
Some numerical methods are introduced in the first term and programmed for the computer using FORTRAN IV. Concepts of Numerical Errors. Methods in Interpolation, numerical integration, solution of nonlinear equations, linear systems of equations.
In the second term non-numeric computing is introduced including simulation, the concept of a list and elementary list processing techniques, sorting, symbol manipulation.
2 hours lectures, | hour problems.
MATH 243 Statistics for the Sciences
The topics of Mathematics 233 with particular emphasis on the analysis and interpretation of experimental data and the design of experiments in the Sciences. The more difficult mathematical techniques associated with these problems will be omitted and many examples from Physics, Chemistry, Biology and other natural Sciences will be considered.
2 hours lectures, 1 hour laboratory.
MATH 300 Discovery and Invention in Mathematics
The art and technique of problem solving from the point of view of discovery and invention (heuristic); induction, analogy, pattern generalization, analysis, similarity and plausible reasoning. Problems will be selected from various areas of mathematics including Geometry (Euclid to Hilbert), Algebraic Structure (Groups in Algebra and Geometry), Set Theory (point sets, Boolean Algebra) and Logic.
2 hours lectures.
MATH 329 Abstract Algebra
Groups; permutation groups, Lagrange’s theorem, normal subgroups, homomorphisms. Fields. Rings and ideals. Integral domains. 2 hours lectures.
MATH 330 (a) Projective Geometry
(b) Non-Euclidean Geometry. Finite geometries, Distance geometry, convex sets. 3 lectures.
MATH 332 Theory of Functions
The real number system. Uniform convergence. Theory of Fourier series. The complex number system. Analytic functions. The Cauchy theorems. Contour integration. Singularities. Conformal mapping.
3 lectures.
MATH 333 Differential Equations
First order differential equations; existence theorems; singular solutions; solution by Laplace Transforms; numerical methods of solutions; solution in series; hypergeometric, Bessel and Legendre functions; introduction to partial differential equations and integral equations.
2 hours lectures.
MATH 334 Numerical Methods
Finite differences. Solution of equations. Computation with series and integrals. Linear systems and matric methods. Difference equations and relaxation methods, Numerical solution of partial differential equations. Methods employing electronic computers.
2 lectures, 2 hours laboratory.
Faculty of Mathematics
MATH 335 Finite Differences
A theoretical course in the calculus of finite differences to include summation, the differences of zero, numerical integration, the relation between integration and summation. An introduction to difference equations.
2 lectures.
MATH 336 Life Contingencies
(a) An advanced course on problems with single lives. 3 hours lectures, I term. (b) An advanced course on problems with multiple lives; population and multiple decrement theory. 3 lectures, 1 term.
MATH 338 Mathematical Statistics
An advanced mathematical course including the multivariate normal distribution and related distributions. Normal Regression Theory. Application .to hypothesis testing and analysis of variance. Maximum likelihood andlarge sample theory.
Prerequisite: Mathematics 233 or equivalent.
2 hours lectures.
MATH 340 Computer Systems
A discussion of the hardware and software required in a computer system. Overlapped channels, interrupt facilities, memory protection, buffers, input-output control systems, macro-programming, monitor systems. Relocation schemes, multi-programming, multi-processing, dynamic memory allocation, timesharing. Special purpose computer systems and simulation of computer systems. Peripheral equipment. Introduction to the theory of sequential machines and the logical design of computers.
2 lectures.
MATH 341 Abstract Algebra
Lattices; groups, Lagrange’s Theorem, normal subgroups, homomorphisms, permutation groups; rings, ideals and integral domains; modules, tensor products; fields and extensions.
3 hours lectures.
MATH 342 Real Variable Theory
Real number system; metric space setting for ideas of continuity, uniform continuity, compactness, convergence, open sets, closed sets, connected sets. Cantor ternary set. Stone-Weierstrass theorem, uniform convergence, equicontinuity. Ascoli’s theorem, fixed point theorems and applications, tangent spaces, differential forms, exterior differentiation, Stokes’ Theorem. Introduction to Lebesgue integration.
2 hours lectures.
MATH 343 Complex Variable Theory
Complex numbers; continuity and differentiability, Cauchy-Riemann equations; solution of Laplace equation; bilinear transformations and conformal mapping; power series; integral theorems, Taylor and Laurent expansions; calculus of residues; series solution of differential equations; theory of Laplace transforms; solution of differential equations by integrals.
2 hours lectures.
MATH 344 Point Set Topology
Topological spaces. Cartesian products, continuous mappings, separation axioms, connectedness. Compact and locally compact spaces, metrizability.
3 hours lectures, 1 term.
MATH 345 Topics in Pure Mathematics for Combinatorial Mathematicians
Elementary introduction to cardinal and ordinal numbers; convexity and its applications to optimization; introduction to the main concepts of projective geometry, metric and topological spaces.
MATH 351 Introduction to Graph Theory and Combinatorical Analysis
Graphs, paths, arcs, circuits, connected graphs, trees, spanning trees, digraphs, Euler paths, tournaments, complete paths in tournaments, factors of bipartite graphs, Menger’s Theorem and flows in networks, theory of enumeration, generating functions, Ramsey’s Theorem and applications, systems of distinct representatives, Latin squares, balances incomplete block designs and (v. k. \) configurations. Applications to practical problems and other areas of mathematics.
MATH 352 Mathematical Operations Research
Review of mathematical techniques frequently used in Operations Research; including Monte Carlo Methods, difference equations, Lagrange Multipliers, generating functions, Riemann-Stieltjes integration, Laplace transforms. Introduction to Linear programming, dynamic programming, activity scheduling, queueing and simulation. Applications to production planning, inventory problems, growth and survival models, scheduling problems, replacement policies and reliability optimization of complex systems.
2 hours lectures.
MATH 360 (a) Tensor Analysis
Vector analysis in curvilinear coordinates; gradient, divergence, curl. Transformation laws of covariant, contravariant, relative tensors. Covariant and intrinsic differentiation. The Riemann-Christoffel tensors, Bianchi identities, Ricci and Einstein tensors. Integrability theorems. Applications to classical mechanics and elasticity. Introduction to general relativity.
2-hours lectures, Fall term.
(b) Differential Geometry. The metric tensor, and elementary differential geometry of surfaces, Introduction to Riemannian geometry; Riemannian curvature, Gaussian curvature and Einstien curvature tensors. Spaces of affine connection and Finsler spaces with application to electromagnetic theory.
2 hours lectures, Winter term.
MATH 361 (a) Calculus of Variations
Euler-Lagrange Equations, Legendre and Jacobi condition, the E-function. Fields of extremals and sufficient conditions; Hibert’s invariant integral. Parameter invariant single and multiple integral problems; Hamilton-Jacobi theory. Introduction to optimal control problems; introduction to direct methods and partial differential equations.
2 hours lectures, Fall term.
(b): Mechanics II. Hamilton's principle. Lagrangian and canonical Equations of mo-
tion. Relativistic mechanics. 2 hours lectures, Winter term.
Faculty of Mathematics
MATH 363 Differential Equations
Boundary value problems of Sturm-Liouville. Green’s Functions. Representation of some physical phenomenon by partial differential equations in the two variables. Separation of variables. Bessel function and Legendre polynomials. Fourier integrals and their associated transforms, e.g. Laplace transform. Integral Equations.
2 hours lectures.
MATH 399 Reading in Mathematics
MATH 410 Modules and Ring Theory
Rings, Modules, Algebras. Types of Rings and Modules. Ideals, Chain Conditions, Radicals, Semi-simple and simple rings and modules. Wedderburn’s Theorem and its generalizations. Krull-Schmidt decompositions. Local Rings and structure of commutative Noetherian Rings. Types of Algebras and Graded Algebras. Goldie’s Structure Theory. Golad-Shafarevitch Theorem.
2 hours lectures.
MATH 411 Group Theory
Elementary properties of Abelian groups, solvable groups, nilpotent groups. Direct products and semi-direct products. Free groups and free products. Elements of group representations.
2 hours lectures.
MATH 412 Galois Theory
Normal extensions. Separable and inseparable extensions. Fundamental theorem of Galois theory. Cyclotomic fields. Solvability in radicals. Kummer fields. Finite fields. Field polynomials, norm and trace. Noether’s equations. Hilbert’s Theorem 90. Infinite Galois Theory.
2 hours lectures.
MATH 413 Non-linear Differential Equations
Riccati equation, conflict and pursuit problems, elliptic integrals and functions, phase plane, non-linear mechanics. Non-linear integral equations.
2 hours lectures.
MATH 425 Introduction to the Theory of Numbers
2 lectures.
MATH 426 Topology
Continuation of general topology. Topological manifolds, a weak embedding theorem, classification of !-manifolds. Triangulation, simplicial complexes, simplicial homology. Classification and homology groups of closed (triangulated) 2- manifolds. The fundamental group covering spaces, homotopy groups, the Hurewicz isomorphism theorem.
2 lectures.
MATH 427 Graph Theory
Graphs and subgraphs. Connection modulo a subgraph. Trees, atcs, and polygons. Separation. 3-connection. The structure of 2-connected graphs. Planar graphs, Kuratowski’s theorem.
2 hours lectures.
MATH 428 Lattice Theory
Ordered sets, lattices, Galois connections. Special attention is given to geometric lattices (matroid theory).
Prerequisite: Mathematics 230.
2 hours lectures.
MATH 429 Combinatorial Topology
Homology theory of complexes. Theorems of invariance, covering, and duality.
Prerequisite: Mathematics 230.
2 lectures, | term.
MATH 430 Finite Projective Geometries
Representations by fields, groups, and algebras. Finite. Euclidean geometries. Sub-geometries. Collineation groups. Factical configuration.
2 lectures.
MATH 432 Functions of a Complex Variable
Analytic continuation. The Riemann surface. Entire, meromorphic functions. Function spaces. Linear operators. 2 hours lectures.
MATH 433 Metric Spaces and Integration
Theory of metric spaces, completeness and compactness, measure in Euclidean n-space, the Lebesgue integral, convergence theorems, the Fubini theorem, differentiability, absolute continuity. A study of Banach spaces.
2 lectures.
MATH 434 Differential Equation of Mathematical Physics
Boundary-value problems. Orthogonal functions. Bessel functions. The Legendre polynomials. The Fourier integral. The Laplace transform. The wave equation.
2 lectures, | hour problems.
MATH 435 Laboratory
Numerical problems arising in actuarial science and statistics. 2 hours laboratory.
MATH 436 Mathematical Logic
An informal introduction to the logic of sentences and predicates, with emphasis on analogies with familiar mathematical structures. Syllogisms and algebra of sets related to predicate logic. Simplification, logical deduction, duality, consistency and completeness. The concepts of constant, variable, function, and set. Axiomatics.
2 lectures.
MATH 437 Construction of Contingency Tables
(a) Accidental death and disability benefits. Pension fund mathematics. Methods of analysing data to produce raw rates for mortality tables. 2 hours lectures, 1 term. ‘
(b) Methods of graduating mortality tables. 2 hours lectures, 1 term.
MATH 438 Estimation and Hypothesis Testing
The mathematics and logic of estimation and hypothesis testing. Consistency, efficiency and sufficiency of estimates, Fiducial and confidence intervals, likelihood, Bayes’ theorem, tests of significance.
2 hours lectures.
Faculty of Mathematics
MATH 439 Theory of Experimental Design
The logic of experimental design with reference to randomization, experimental and sampling errors. Construction and analysis of various kinds of designs.
2 hours lectures.
MATH 440 Probability
Classical probability and introduction to stochastic processes with applications such as branching processes, epidemics, etc. 2 hours lectures.
MATH 441 Quantum Mechanics
The Schroedinger wave equation, interpretation of wave functions, harmonic oscillator in wave mechanics. The hydrogen atom. Perturbation theory. The variation methods. The W.K.B. approximation.
2 lectures.
MATH 442 Theory of Relativity
Covariant and contravariant tensors. Riemannian space. Gaussian curvature. The ‘Lorentz transformation and Einstein’s special theory. Introduction to the general theory of relativity.
2 lectures, Winter term.
MATH 443 Electromagnetism
Applications of the Maxwell equations. Refiection and refraction. Introduction to wave guides and antennae. 2 lectures, Fall term.
444, Elasticity. Problems in stress and strain. Isotropic bodies. Equilibrium equations. Torsion and flexure. 2 lectures, Winter term.
MATH 445 Hydrodynamics
Continuous and discontinuous flow. Aerofoil theory. Viscous flow. 2 lectures.
MATH 446 History of Mathematics
The development of Mathematics from ancient to modern times, including study of prominent mathematicians and their works. Problems will be worked using both modern and historical approaches.
2 lectures.
MATH 447 Statistical Mechanics
Applications of probability theory to theoretical Physics. 2 lectures, Fall term.
MATH 448 Differential Geometry
Curves in space. Gaussian curvature. Tensorial notation. Introduction to differentiable manifolds. 2 lectures.
MATH 449 Experimental Design
Similar to Mathematics 439 but with more accent on the logic and methods than on the mathematics. Primarily for students in the Sciences. 2 hours lectures.
MATH 450 Applied Analysis
Applied Mathematics for Science majors. Ordinary and partial differential equations. Laplace and Fourier transforms. Special functions. Fourier series, Vector and matric methods. Calculus of variations. Other topics in advanced calculus.
2 lectures.
MATH 451 Optimization
Discrete functions; continuous functions of n variables. Quadratic forms; convex functions. Equality constraints; Lagrange multipliers and generalizations. Inequality constraints, Kuhn-Tucker theorem. Steepest descent and gradient methods. Fibonnaci search, successive approximations, simplex method and other techniques. Applications to the solution of equations and non-linear regression.
2 hours lectures.
MATH 452 Linear Programming
Mathematical foundations. Simplex method and revised simplex method. Duality. Computational methods. Assignment and transportation problems. Integer Programming. Applications to game theory, industrial problems and economic theory.
2 hours lectures.
MATH 433 Queueing Theory
Input and Service-time distributions; Poisson process, Erlangian distribution. Single channel queue; differential-difference equations, integral equations. Complex queueing models. Monte Carlo techniques.
2 hours lectures.
MATH 454 Game Theory
Classification of games. Zero-sum matrix games. Infinite zerosum games. n-person co-operative and non-co-operative games. 2 hours lectures.
MATH 455 Mathematical Programming
An introduction to the methods and applications of integer programming, non-linear programming and dynamic programming. 2 hours lectures.
MATH 457 Applied Combinatorial Mathematics
May include any subset of the following topics: applications of combinatorial mathematics to optimization, selected topics from the Beckenbach book, structural models, graphs and electrical networks, graph theory and statistical mechanics, the Ising problem, percolation processes, the dimer problem, random walk, applications to chemistry, automata.
2 hours lectures.
MATH 458 Topological Graph Theory
Selected topics within the general area of graphs and maps in the plane and on other surfaces, the four colour problem, connectivity and separation in graphs, thickness and genus of graphs, etc.
2 hours lectures.
MATH 459 Algebraic Graph Theory
Graphs and mairoids. Applications of algebraic techniques (e.g. matroids, matrices, chain groups) to graph theory or related combinatotial topics. Applications of graph theory to algebra.
2 hours lectures.
Faculty of Mathematics
MATH 460 Combinatorics
Enumerative mathematics. Combinatorial properties of various mathematical structures (e.g. graphs, geometries, etc.). 2 hours lectures.
MATH 461 (a) Advanced Actuarial Theory
(a) Risk Theory. Individual and collective risk theory. Ruin theory. Stop-loss reinsurance premiums. Monte Carlo methods. 2 hours lectures, | term.
(b) Actuarial Laboratory. A tutorial course for the advanced actuarial student. 2 hours problems, | term.
MATH 462 (a) Fourier Series and Orthogonal Functions
Linear spaces, orthogonal functions, Fourier series, Legendre and Bessel functions, harmonic analysis. 2 hours lectures, Fall term.
(b) Measure and Integration. The theory of measure and the Lebesgue integral. 2 hours lectures, Winter term.
MATH 463 Control Theory: The theory of controlled processes
Optimal control. Stability. Lyapunov’s direct method. 2 lectures, Fall term.
MATH 470 Numerical Solution of Ordinary and Partial Differential Equations
Existence and uniqueness of solutions of ordinary differential equations, one-step methods for scalar and systems of differential equations, multi-step methods, linear boundary value problems. Discrete approximations to partial differential equations, convergence, stability and convergence rate estimates, generalization to non-linear equations.
2 hours lectures.
MATH 471A Switching Circuits. Switching devices. Binary codes and arithmetic. Boolean
algebra and its application to switching circuits. Cononical forms for Boolean functions. Simplification of switching functions. Analysis of sequential circuits. Synchronous and asynchronous operation. Design of sequential circuits.
2 hours lectures, Fall term.
MATH 471B Introduction to Digital Computer Science
Organization of a general purpose computer. Component systems. Hardware, system design and software. Storage cells, memories, logic circuits, counters, sequence generators, decoding networks. Number systems and codes. Elementary digital machines. Registers and register transfers. Arithmetic and control functions. Design of simple machines. Stored program computers. Memory, arithmetic unit, control and input-output equipment. Instruction and data formats. Implementation of arithmetic and program instructions. Jump instructions, subroutines, index registers. Machine language programs. Overall logical design. Algorithms for arithmetic operations. Design of fast adders. Parallel arithmetic units. Fast multiplication and division. Floating point arithmetic. Residue number codes.
Prerequisite: Switching Circuits.
2 hours lectures, Winter term.
MATH 472B Introduction to Automata Theory
Sequential machine models. Reduction of completely and incompletely specified machines. Realization of machines. The secondary assignment problem. Decomposition of machines. Finite automata and regular events. Introduction to Turing machines and computability. Introduction to formal languages.
Prerequisite: Switching Circuits.
2 hours lectures, Winter term.
MATH 480 Functional Equatiens
Cauchy's, Pexider’s and similar equations. Equations for polynomials and for trigonometric functions. Reduction to differential equations. General methods and theorems. Iteration. Applications. Further topics, as Equations for functions of several variables, or Equations for analytic functions, or Equations on algebraic structures.
2 hours lectures.
499, Reading in Mathematics.
Faculty of Mathematics
Graduate and Research Programmes
While the faculty offers graduate work over a broad specirum of the various branches of Mathematics, fields of special interest include: Abstract Algebra, Combinatorial Analysis, Computer: Science, Differential Equations, Differential Geometry, Foundations, Functional Analysis, Functional Equations, Graph Theory, Harmonic Analysis, Mathematical Logic, Number Theory, Numerical Analysis, Optimization, Probability, Statistical Inference, Switching and Automata Theory.
The University of Waterloo has at present four computer systems, namely an IBM System /360 Model 75, an IBM System /360 Model 44, an IBM 1710, an IBM 1620 and peripheral equipment which includes an IBM 2250 Graphic Display and a CAL- COMP 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.
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 calendar pertaining to the Graduate Studies. Students proceeding to the M. Math. degree are encouraged to present theses. Those proceeding by course work must submit a substantial essay in connection with at least one of the courses.
Applied Analysis and Computer Science: Faculty members of the Applied Analysis and Computer Science Department are currently engaged in research in a number of areas including: Computer Graphics, Formal Languages, Switching Theory, Theory of Automata, Numerical Analysis, Information Theory, Functional Equations, Compiler Construction, and Programming Systems.
Research in compiler construction has produced the WATFOR fast FORTRAN IV compiler currently being used by over one hundred System /360 Computing Centres throughout the world. Over seventy installations are using a similar compiler developed in 1965 for 7040-7044 Series machines (Communications of the ACM, January, 1967).
The problems investigated in the areas of formal languages, automata and switching theory include: context-free languages, regular languages and finite automata, structure theory of sequential machines, asynchronous sequential circuits, and design of arithmetic units for residue number systems.
A graphic display unit will permit research in new techniques in graphic programming, design procedures and analogue simulation. A process contro] computer is currently used to perform and analyze complex experiments, some of which would not be undertaken if only conventional methods were available.
In numerical analysis, algorithms for two-point boundary problems, stiff systems of differential equations, unilateral matrix equations and optimization problems are under investigation at the present time.
In applied Analysis, among others, functional equations are studied, i.e. the theory of determining functions from elementary equations containing them. It is a field of mathematics with a two century history although the somewhat more general theory has developed only in the last two decades. Functional equations have applications in many modern disciplines including information theory, mathematical psychology and universal algebra.
At the University of Waterloo the research being done in functional equations includes general methods of solution, uniqueness theorems and applications in differential geometry, homological algebra, functional analysis, theories of continuous groups, quasigroups and nets, complex functions, nomographs and the theory of distributions.
Applied Mathematics: Research in this department is being carried out in a number of areas directly or indirectly applicable to problems in the Physical Sciences. The range of interests of the members of the department reflects the diversity of problems of a mathematical nature which arise in the real world.
The major areas of specialization include Nonlinear Differential Equations, Spectral Theory of Differential Operators, Optimal Control] Theory, Boundary Layer Problems in Fluid Dynamics, Harmonic Analysis, Theory of Relativity, Particle and Quantum Physics, Statistical Mechanics and the Theory of Liquids.
Pure Mathematics: Current research in this area includes studies in sheaf theory and categories, differential geometry, topology of differentiable manifolds, Homotopy theory, function algebras, theory of generalized decomposition of groups, theory of integration and measure, topological vector spaces, Banach algebras, logic and foundations of set theory.
Statistics: 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.
Closely related to this research, there is active interest in problems of experimental design, with particular reference to incomplete designs, multivariate analysis, estimation theory, mathematical genetics and stochastic processes.
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-chromatic graphs and the Ramsey numbers.
Increasing contact with the departments of Chemistry, Physics and Psychology 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.
Faculty of Mathematics
Graduate Courses
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703.
705.
707.
715.
716.
718.
719.
720.
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768.
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.
Linear Algebra.
Galois Theory.
Topics on Rings and Fields. Differential Geometry. Differentiable Manifolds.
Topological and Lie Groups.
MATH 778 Special Topics in Geometry
MATH 779 Topics on Topological Structures
MATH 780 Combinatorial Analysis
MATH 782 Combinatorial Graph Theory
MATH 783 Analytic Graph Theory
MATH 784 Linear Graphs
MATH 785 Planar Graphs
MATH 786 Extrema in Graphs
MATH 787 Directed Graphs
MATH 789 Matroid Theory
MATH 796 Seminar in Graph Theory
MATH 797 Topics in Graph Theory
MATH 798 Seminar in Combinatorial Analysis
MATH 799 Topics in Combinatorial Analysis
MATH 810 Harmonic Analysis
MATH 811 Orthogonal Series
MATH 815 Special Functions
MATH 817 Abstract Measure Theory
MATH 819 Functional Analysis
MATH 820 Linear Operators
MATH 828 Topics in Classical Analysis
MATH 829 Topics in Functional Analysis
MATH 830 Potential Theory
MATH 832 Ordinary Differential Equations
MATH 834 Introduction to Partial Differential Equations
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849.
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852.
855.
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860.
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891.
Faculty of Mathematics
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 for Analytic Functions. Integral Equations.
Seminar on Functional Equations.
Topics on Functional Equations.
Calculus of Variations.
. Analytic Theary of Geometric Objects.
Vector and Tensor Analysis.
Integral Transforms.
Theory of Approximation.
Introduction to Numerical Analysis.
Numerical Solution of Ordinary Differential Equations. Numerical Methods in Linear Algebra.
Numerical Solution of Partial Differential Equations. Problems in Numerical Integration.
Seminar in Numerical Analysis.
Topics in Applied Analysis.
Topics in Numerical Analysis.
Computer Programming.
Advanced Programming Systems.
MATH 892 Advanced Computer Techniques
MATH 894 Finite Automata
MATH 895 Design of Sequential Machines
MATH 896 Algebraic Structure of Sequential Machines
MATH 897 Automata and Languages
MATH 899 Statistical Information Theory
MATH 900 Measurement of Information
MATH 905 Seminar in Computer Science
MATH 908 Topics in Computer Science
MATH 909 Topics in Information Theory
MATH 910 Introduction to Random Variables
MATH 911 Theory of Probability
MATH 912 Stochastic Processes
MATH 918 Seminar in Probability Theory
MATH 919 Topics in Probability Theory
MATH 925 Mathematical Genetics
MATH 927 Topics in Probability and Biometry
MATH 929 Topics in Biometrical Statistics
MATH 930 Foundations of Statistics
MATH 932 Advanced Statistics
MATH 934 Applied Statistics
MATH 938 Seminar in Statistics
MATH 939 Topics in Statistics
MATH 950 Complex Variable Techniques in Physical Problems
MATH 951 Group Theory in Physical Problems
Faculty of Mathematics
MATH 969 Topics in Applied Mathematics
MATH 970 Mathematical Optimization
MATH 971 Applications of Directed Graphs
MATH 972 Mathematical Programming
MATH 973 Network Programming
MATH 975 Mathematical Operations Research
MATH 976 Seminar in Mathematical Operations Research
MATH 978 Seminar in Optimization
MATH 979 Topics in Optimization
MATH 990 Data Processing for Behavioral Scientists
MATH 992 Mathematical Methods for Science and Engineering
MATH 994 Numerical Methods and Programming
995, Seminar in Mathematics Education.
MATH 996 Topics in Mathematical Education
MATH 999 Topics in the History of Mathematics
M690. Literature and Research Studies.
M696. M. Math. Thesis.
M697. M. Phil. Thesis.
M699. Ph.D. Thesis.