88 courses in the 1964–65 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
Faculty listed in 1964–65
R. G. Stanton, B.A. (Western), M.A., Ph.D. (Toronto), F.S.S. Professor and Chairman of Department Dean of the Faculty of Graduate Studies
K. D. Fryer, B.A. (Western), M.A., Ph.D. (Toronto) Professor and Associate Chairman of Department G. Berman, M.A., Ph.D. (Toronto) - - - - - - Professor W. B. Pennington, M.A., Ph.D. (Cambridge) - - - Visiting Professor D. A. Sprott, M.A., Ph.D. (Toronto), F.S.S. - - - - Professor W. T. Tutte, M.Sc., M.A., Ph.D. (Cambridge), F.R.S.C. - - - Professor G. E. Cross, M.A. (Dalhousie), Ph.D. (British Columbia) - Associate Professor H. F. Davis, S.M., Ph.D. (Massachusetts Institute of Technology) Associate Professor R. A. Staal, M.A., Ph.D. (Toronto) - - - - Associate Professor D. G. Wertheim, B.A. (McMaster), M.A., Ph.D. (Toronto) - Associate Professor C. F. A. Beaumont, B.A. (McMaster), M.A. (Toronto) - Assistant Professor M. Behara, M.Sc. (Utkal), Dr. rer. oec. (Saarland), F.S.S. - Assistant Professor A. Kerr-Lawson, B.A. (Toronto), S.M. (Chicago), Ph.D. (McMaster) Assistant Professor R. C. Mullin, B.A. (Western), M.A. (Waterloo) - - - - Lecturer R. B. Reed, B.A.Sc. (Toronto), M.Sc. (Waterloo) = - - - - Lecturer G. N. Robertson, M.Sc. (Manitoba) - - - - - Lecturer P. L. J. Ryall, B.Sc. (London), M.A. (Cambridge), ASA. - - Lecturer K. Salkauskas, B.A.Sc. (Toronto), M.Sc. (Waterloo) = - - - Lecturer T. W. Troughton, B.A.Sc. (Toronto), M.Sc. (Waterloo), D.I.C. (London) Lecturer
Computer Science Division
J. W. Graham, M.A. (Toronto)
Faculty listed in 1964–65
Associate Professor and Director of Computing Centre D. D. Cowan, B.A.Sc. (Toronto), M.Sc. (Waterloo) - - - Lecturer J. D. Lawson, B.A.Sc. (Toronto), M.Sc. (Waterloo) - - - - Lecturer
Functions and limits, the derivative. Differentiation formulae. Applications to tangents, rates, extrema. 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.
The rational, real, and complex number systems. Polynomial functions. Theory of equations. Determinants. Vector and matric notation. Co-ordinates in 3 dimensions. Systems of planes and lines. Standard equations of quadric surfaces. Spherical and cylindrical co-ordinates.
A continuation of course 12. Infinite series and power series. Partial derivatives. Multiple integration and applications to areas, volumes, centroids, moments. Introduction to differential equations.
Introduction to the use of desk calculators. Simple problems on interpolation, solution of algebraic equations, numerical evaluation of integrals, systems of equations.
Standard methods of solution. Applications to physical and engineering problems. Linear equations with constant co-efficients. Systems of differential equations. Solution by series. Numerical methods of solution. Partial differential equations; applications of partial differential equations.
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.
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.
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, 1 hour problems, one term.
44, Complex Variable. Cauchy-Riemann equations, the Cauchy integral theorems, conformal mapping, the Taylor and Laurent series, contour integration. Prerequisites: Math 33, 34.
Frequency distributions; probability; Binomial, Normal, and Poisson laws. Sampling theory. Distribution of Chi-squared, F, and t. Hypothesis testing, quality control, regression theory. Curve fitting. Analysis of variance, introduction to experimental design.
The Heaviside Calculus and the Laplace Transform. Admittance, impedance, and other operators. Applications of operator techniques to problems in electricity, mechanics, and heat.
Prerequisites: Math 22, 31, and consent of instructor.
MATH 54Differential Equations of Mathematical Physics
The wave equation. Potentials. Boundary-value problems. Eigenvalue problems. Expansions in series of orthogonal functions. Spherical, cylindrical, and ellipsoidal harmonics. Prerequisites: Math 22, 31, and consent of instructor.
Fundamentals of digital computers, including memory types, arithmetic compononents, input-output and control units. Binary numbers, floating-point arithmetic, flow charting, machine-language coding. Automatic coding, including assemblers, compilers, and translators. Interpretive routines.
The distance formula. Functions and their graphical representation. The linear function. Forms of the line equation. The quadratic function and roots of quadratic equations. Algebraic and geometric approach to loci. Standard forms for the circle, parabola, ellipse, hyperbola. The number system. Polynomial functions. Remainder theorem. Functions of more than one variable. Equations in one or more variables. The general trigonometric functions, their values and graphs. Radian measure. Compound angle formulae. Trigonometric formulae. Trigonometric equations. The sine and cosine laws for triangles. The logarithmic function. The laws of logarithms. Arithmetic and geometric series. The binomial series. Properties of the binomial coefficients. Permutations and combinations.
A terminal course designed for Arts students who wish to learn something of the fundamental ideas of mathematics but who will not be encountering technical problems of application. The course will include discussion of the fundamental concepts involved in a selection of topics chosen from mathematical areas such as Calculus, Statistics, Probability, Projective Geometry, Non-Euclidean Geometry, Set Theory, Group Theory, Field Theory, Boolean Algebra, Mathematical Logic, Vector Spaces, Matrices, Numerical Analysis.
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.
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.
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.
Methods of formal integration. Differential equations. Fourier series. Riemann integration and applications. Calculus of variations. Line integrals. Stokes’ and Green’s theorems.
Frequency distributions. Probability. Binomial, Normal, and Poisson laws. Sampling theory. Curve fitting. Distributions of Chisquared, F, and t. Hypothesis testing. Quality control. Regression theory. Analysis of variance. Introduction to experimental design.
The theory of compound interest and of life contingencies. An elementary course on the mathematics of investment and on applications of probability to problems of life and death. Annuities, single and annual premiums. Reserves. Standard actuarial notation.
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.
The nine-points circle. The Simson line. Cross ratio. Projection. Harmonic ranges and involutions. Properties of circles. Axioms of incidence for projective geometry. Duality. Theorems of Pappus and Desargues. Introduction of co-ordinates. Conic sections. Introduction to non-Euclidean geometry.
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.
First-order differential equations. Linear equations with constant coefficients. Solutions in series. Systems of differential equations. Introduction to partial differential equations. Introduction to integral equations.
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.
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.
An advanced mathematical course including the multivariate normal law and related distributions. Normal regression theory. Applications to hypothesis testing and analysis of variance.
Topological concepts. Analytic continuation. The Riemann surface. Entire meromorphic functions. Periodic functions. Special functions. General metric spaces. Function spaces. The integral as an operator.
Theory of metric spaces, completeness and compactness, measure in Euclidean n-space, the Lebesque integral, convergence theorems, the Fubini theorem, differentiability, absolute continuity.
An informal introduction to the logic of sentences and predicates, with emphasis on analogies with familiar mathematical structures. Syllogisms and the algebra of sets related to predicate logic. Simplification, logical deduction, duality, consistency and completeness. The concepts of constant, variable, function, and set. Axiomatics.
The mathematics and logic of estimation and hypothesis testing. Information. Consistency. Efficiency. Sufficiency. Fiducial and confidence intervals. The problems of large and small samples. 2 lectures.
The logic of experimental designs. Randomization. Experimental and sampling errors. Mathematical methods of constructing various designs. Applications to problems in the sciences.
Covariant and contravariant tensors. Riemannian space. Gaussian curvature. The Lorentz transformation and Einstein’s special theory. Introduction to the general theory of relativity.
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.
Logic of experimental designs. Randomization. Experimental and sampling errors. Designs applied in biology. Methods of analysis for factorial designs, Latin squares, etc.
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.
Finite differences, with stress on operator methods and central difference notation. Iterative procedures for solution of equations. Computations involving integrals. Error estimation. Curve fitting and orthogonal polynomials. Gaussian quadrature. Methods of solving ordinary and partial differential equations. Eigenvalue problems for systems of linear equations and for differential equations. Matric methods in applied mathematics.
Concepts from thermodynamics. One-dimensional gas dynamics. One-dimensional wave motion. Waves in supersonic flow. Flow in ducts and wind tunnels. Methods of measurement. Equations of frictionless flow. Small-perturbation theory. Bodies of revolution and slender body theory. The similarity rules of high-speed flow. Transonic flow. The method of characteristics. Effects of viscosity and conductivity. Laminar and turbulent boundary layers. Concepts from gas kinetics.
Elliptic functions. The hypergeometric function. The gamma and beta functions. The functions of Laplace, Legendre, Lamé, Mathieu, and Bessel. Orthogonal functions; the functions of Laguerre, Hermite, Chebyshev.
Review of classical probability theory, including occupancy problems, the binomial, Poisson, and nomal distributions, applications in physics. Recurrent events. Markov chains, stochastic processes, including the ruin problem and diffusion processes; application to information theory, radar, queuing problems, etc.
General concepts of computer types and applications. Flow charting. Coding, instruction formats. Editing. Storage elements and buffers. Control and accuracy in digital computers. Input and output devices and their use. Number systems. Automatic programming and universal computer languages. Logic and Boolean Algebra. Heuristic programming. Elements of logical design.
Vector spaces, linear transformations, matrices. Euclidean spaces, groups of transformations, algebra of tensors; covariant differentiation, divergence, Laplacian, curl. Generalizations to Riemannian spaces. Applications to other fields including differential geometry, mechanics, elasticity, hydrodynamics, electricity, and general relativity.
Non-numeric computing. List processors and their application to the calculation of recursive functions, language translation, analytic differentiation and integration, mathematical logic, sorting, heuristic programming. Polish strings. Simulation of a List Processor.
MATH 641Mathematical Methods for Operations Research
Construction and analysis of mathematical models of systems and processes connected with Science and Engineering. Related topics in numerical methods, probability, statistics, and linear graph theory. Special methods such as simulation, queuing theory and: renewal theory. Methods of optimization including linear and non-linear programming, steepest descent, dynamic programming, and game theory.
664, Calculus of Variations. The Euler equations and the Legendre and Jacobi conditions. The Weierstrass E function and sufficient conditions. The theory of transversals and isoperimetric problems. Hilbert’s existence theorem. Selected topics from the theories of Kneser and Caratheodory; the problem of Bolza.
W. B. Fallis, M.A.Sc., Ph.D. (Toronto) - Professor and Chairman of Department S. Alpay, Dipl. Ing., Dr. Ing. (Berlin) - - - - - Professor G. T. Csanady, Dipl. Ing. (Munich), Ph.D. (New South Wales) - - Professor G. F. Pearce, B.A.Sc. (British Columbia), M.A.Sc. (Toronto) Associate Professor