79 courses in the 1963–64 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
R. G. Stanton, B.A. (Western), M.A., Ph.D, (Toronto) Professor and Chairman of the Department, Dean of the Faculty of Graduate Studies
G. Berman, M.A., Ph.D. (Toronto) - = es eee Professor K. D. Fryer, B.A. (Western), M.A., Ph.D. (Toronto), - - - «+ Professor D. A. Sprott, M.A., Ph.D. (Toronto) - - - - - - Professor W. T. Tutte, M.Sc., M.A., Ph.D. (Cambridge) - - - Professor
H. F. Davis, S.M., Ph.D. (Massachussets Institute of Technology), Asssociate Professor
M. A. McKiernan, M.A. (Loyola), Ph.D. (Illinois Institute of Technology) Associate Professor
R, J. Semple, M.A. (Toronto), Ph.D. (Princeton) - + 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 J. W. Graham, M.A. (Toronto) - = © = «= ~ Assistant Professor A. Kerr-Lawson, B.A. (Toronto), S.M. (Chicago) - - Assistant Professor D. D. Cowan, B.A.Sc. (Toronto), M.Sc. (Waterloo) ~ - - - Lecturer J. D. Lawson, B.A.Sc. (Toronto), M.Sc. (Waterloo) - - - - Lecturer R. C. Mullin, B.A. (Western), M.A. (Waterloo) - - - - - Leeturer H. I. McIntosh, B.A. (Toronto), F.S.A. - © © = Lecturer (Part-time) R. B. Reed, B.A.Sc. (Toronto), M.Sc. (Waterloo) - - - - Lecturer K. Salkauskas, B.A.Sc. (Toronto), M.Sc. (Waterloo) - - - - Lecturer
Operations on polynomials, factoring, fractions, exponents and surds, complex numbers, Functions and graphs, limits, infinity. Linear and quadratic equations, theory of quadratic equations, systems of linear and quadratic equations. Ratio and proportion, variation; inequalities. Sequences, special progressions, sigma notation, the binomial theorem, the infinite geometric and binomial series. Mathematical induction. The remainder theorem. Permutations and combinations.
2 lectures.
Radian measure. Trigonometric functions of acute angles. Identities. Functions of special angles, use of tables, trigonometric equations. Solution of right triangles. Functions of any angle. Graphs of the trigonometric functions. Amplitude, frequency, periodicity. Compound angle formulae, sums and products. Logarithms to an arbitrary base, change of base, common logarithms and their use in computation, exponential equations. Solutions of triangles with and without logarithms Heights and distances in two and three dimensions. Area of a triangle.
2 lectures.
A problems course to accompany courses 6, 7, and 11. Students will work selected problems under supervision. A certain proportion of the problems will extend the work of courses 6, 7, and 11 to include mathematical, for. mulation of physical problems. .
4 hours problems.
Co-ordinates, distance, slope, direction cosines. Forms
of the line equation. Loci. Circles, tangents to circles. Translation and rotation of
axes, The standard equations for the parabola, ellipse, and hyperbola. Tangents to
the conics, Asymptotes. General definition of a conic. Polar and parametric equations. lectures.
12, Calculus I. 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 integartion 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.
3 lectures, 2 hours problems.
Zi. Aigebra and Solid Geomietry. 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.
2 lectures, 1 hour problems.
A continuation of course 12. Infinite series and power series. Partial derivatives. Muitipie integration and applications to areas, volumes, centroids, moments. Introduction to differential equations.
Prerequisite: Math 12.
3 lectures, one term.
Introduction to the use of desk calculators. Simple problems on interpolation, solution of algebraic equations, numerical evaluation of
integrals. systems of equations integrals, systems of equations.
2 hours problems, one term.
A problems course to accompany Math 22. 2 hours problems, one term.
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.
Prerequisite: Math 22.
3 lectures, one term.
Ordinary, divided, and central difference interpola-
tion formulae. Graphic and numerical solutions of algebraic and transcendental uations. Computation with series and integrals. Systems of linear equations. Deter-
minants and matrices. Eigenvalue problems. Iterative procedures, Relaxation methods.
Difference equations. Mathematical principles associated with electronic computers.
Prerequisite: Math 23.
2 lectures, 4 hours problems, one term.
Real numbers, sequences, limits, continuity. The derivative. Generali Theorem of Mean Vaiue. Functions of severai variabies, 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.
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 22, 31.
3 lectures, one term.
Partial differential equations, complex variables, Laplace transform, special functions. Calculus of variations, Fourier series, vector methods, line integrals.
Prerequisites: Math 22, 31.
2 lectures, one term.
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, 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.
2 lectures, 1 hour problems, one term.
Further study in the topics listed for Mathematics 41. Prrequisite: Math 41. 3 lectures, one term.
Frequency distributions; probability; Binomial, Normal, and Poisson laws. Sampling theory. Distribution of Ghisquared, F, and t. Hypothesis testing, quality control, regression theory. Curve fitting. Analysis of variance, introduction to experimental design.
Prerequisite: Math 22.
2 lectures, 3 hours problems, one term.
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.
2 lectures, 1 hour problems, one term.
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.
2 lectures, 1 hour problems, one term.
Fundamentals of digital computers, includ ing memory types, arithmetic components, input-output and control units, Binary numbers, floating-point arithmetic, flow charting, machine-language coding. Automatic coding, including assemblers, compilers, and translators. Interpretive routines. Prerequisite: Math 32.
3 lectures, one term.
Fundamental properties of vector spaces. Matrices as operators in vector spaces. Quadratic forms. Functions of matrices. Applications.
Prerequisite: Math 21.
3 lectures, one term.
The Ontario Grade 13 curriculum will be followed. 3 lectures.
The Ontario Grade 13 curriculum will be ‘ollowed. - : : : : : 3 lectures.
The Ontario Grade 13 curticulum will be followed, omitting the study of Statics, lectures.
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.
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, Coordinate systems.
2 lectures, 1 hour problems.
Introduction to finite differences. Interpolation. Numerical integration. Introduction to the use of electronic computers. 1 lecture, 2 hours problems.
Introduction to the theory of sets and groups. Introduction to rings and fields. Vector spaces and matrices. 3 lectures.
’
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.
Methods of formal integration. Differential equations. Fourier series. Riemann integration and applications. Calculus of variations. Line integrals. Stokes’ and Green’s theorems.
3 lectures.
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.
1 lecture, 2 hours problems.
The theory of frames. Centres of gravity. Moments of inertia. Equilibrium conditions. Gravitational motion. The dynamics of rigid bodies. 2 lectures.
The theory of life contingencies, An elementary course on applications of probability to problems of life and death, Annuities, single and annual premiums, Reserves. Standard actuarial notation.
2 lectures..
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.
COURSE DESCRIPTION.
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.
3 lectures.
A continuation of course 230, 2 lectures.
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.
2 lectures.
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.
A theoretical course in the calculus of finite differences to include summation, the differences of zero, numerical integration, the relation betwen integration and summation, An introduction to difference equations.
2 lectures.
An advanced course on problems of single lives. 2 lectures.
Vectorial treatment of physical problems. Special examples from three-dimensional statics and dynamics. Introduction to the Lagrange equations, 2 jJectures.
An advanced mathematical course including the multivariate normal law and related distributions. Normal regression theory. Applications to hypothesis testing and analysis of variance.
2 lectures..
Electrostatics and magnetostatics. The theorem of Gauss. Development of the Maxwell equations. lectures.
Representations by fields, groups, and algebras. Finite Euclidean geometries. Sub-geometries. Collineation groups. Tactical configurations. 2 lectures.
A continuation of course 331. 2 lectures. .
Topological concepts. Analytic continuation. The Riemann surface. Entire meromorphic functions, Periodic functions. Special . functions. General metric spaces. Function spaces. The integral as an operator.
2 lectures.
Measure theory. The Lebesgue-Stieltjes integral. Lebesgue integration. lecture.
Boundary-value problems, Orthogonal functions. Bessel functions. The Legendre polynomials. The Fourier integral. The Laplace transform. The wave equation.
2 lectures, 1 hour problems.
Numerical problems arising in actuarial science and statistics. 2 hours laboratory.
An advanced course on the death and survival of multiple lives. 2 lectures.
437; Graduation and Mortality. Methods of constructing and graduating mortality tables. 1 lecture.
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.
2 lectures.
Recurrent events. Markov processes and applications to Physics and Biology, including diffusion processes and epidemics. 2 lectures.
The classical mechanics of Lagrange and Hamilton. Introduction to quantum theory. 2 lectures.
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.
Applications of the Maxwell equations. Reflection and refraction. Introduction to wave guides and antennae. 2 lectures.
444, Elasticity. Problems in stress and strain. Isotropic bodies. Equilibrium equations, Torsion and Flexure. 2 lectures.
445, Hydrodynamics. Continuous and discontinuous flow. Aerofoil theory. Viscous flow. 2 lectures.
446, History 01 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.
Applications of probability theory to theoretical
Physics. 2 lectures.
Curves in space. Gaussian curvature. Tensorial notation. Introduction to differential manifolds, 2 lectures.
Logic of experimental designs. Randomization. Experimental and sampling errors. Designs applied in biology. Methods of analysis for pectorial designs, Latin squares, etc.
lectures.
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.
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 equatoins. 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 highspeed 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 normal 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.
621, Computer Programming. 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.
half course.
‘CURRICULA AND COURSES OF STUDY 624, Advanced Statistics.
Operational mathematics. Laplace transforms. Computer approximations for algebraic and transcendental functions. Numerical integration. Operations research models. Simplex method of linear programming. Convex programming. Dynamic programming. Monte Carlo techniques. Information theory and transmission. Information retrieval..
Review of the mathematics used in model making. Methods of optimization, including linear programming and game theory. Applications to business, industrial, and military problems, including inventory replacement and allocaticn models, queuing theory, and decision theory.
664, Calculus of Variations. The Euler equations and the Legendre and Jacobi conditions. The Weierstrass E function and sufficient conditions. The theory of trans-
versals and the isoperimetric problems. Hilbert’s existence theorem. Selected topics from the theories of Kneser and,Caratheodory; the problem of Bolza.
-Definitions and[basic theorems. Planar graphs and Kuratowski’s Theorem. Selected topics from*advanced graph theory.