66 courses in the 1981–82 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
Mathematics Course Descriptions Notes
1. Certain core Mathematics courses are offered at three different levels. The advanced level courses are intended for exceptionally gifted students in an Honours programme. A student pursuing an Honours degree may substitute the corresponding Advanced level course(s) for any required Honours level course(s).
Similarly, a student pursuing a Pass or General degree may substitute the corresponding Honours level course(s) for any required General level course(s), unless the student has been required by the Standings & Promotions Committee to switch from an Honours programme to General or Pass. In this case, the student must enrol in General level courses. The following table sets out corresponding advanced/honours/general courses.
Advanced Honours General
Math 120a/b Math 124a/b Math 220a/b
Math 140a/b Math 144a/b Math 240a/b
Math 130a/b Math 134a/b Math 230a/b
Math 241a/b Math 231a/b Math 221a/b Math 244a/b Math 234a/b Math 224a/b P Math 341a/b = Math 331a/b Math 321a/b _— Math 334a Math 324a
MATH 103Introductory Algebra (For students in Arts/Social Sciences)F 3C,1T 0.5
An introduction to applications of algebra to business, the behavioural sciences, and the social sciences. Topics will be chosen from set theory, permutations and combinations, binomial theorem, probability theory, systems of linear equations, vectors and matrices, mathematical induction.
N.8.: Not open to students in the Faculty of Mathematics. Math 103 does not cover all the material normaily included in Grade 13 Algebra; however, superior performance (approximately 80%) would probably provide an adequate background for most courses that demand Grade 18 Algebra as a prerequisite (e.g. Math 124a). Grade 12 Mathematics is recommended.
MATH 104Introductory Calculus (For students in Arts/Social Sciences)W 3C0,1T 0.5
An introduction to applications of calculus in business, the behavioural sciences, and the social sciences. The models chosen will include the study of polynomial, rational, exponential and logarithmic functions; elementary analytic geometry; linear and quadratic systems of equations. The major concepts introduced to solve problems are: rate of change; optimization; growth and decay; and integration. N.B.: Not open to students in the Faculty of Mathematics. Math 104 does not cover all the material normally included in Grade 13 Calculus; however, superior performance (approximately 80%) would probably provide an adequate background for most courses that demand Grade 13 Calculus as a prerequisite (e.g. Math 120a). Grade 12 Mathematics is recommended.
MATH 105Mathematics (For Environmental Studies Students)F 3C 0.5
Quantitative analysis in environmental research. Elementary concepts in Algebra: notation, terminology, operations. Probability Theory. Permutations and Combinations, approaches to probability, dependent and independent events, conditional probability, distribution functions, including the Binomial, Poisson and Normal distributions, with applications to problems in Environmental Studies.
Prereq: None
N.B.: Not open to students in the Faculty of Mathematics
MATH 106Mathematics (For Kinesiology Students)F 3C,1T 0.5
Algebraic functions and their graphs; exponential and logarithmic functions; elementary differential and integral calculus; applications and problems associated with kinesiology.
N.B.: Not open to students in the Faculty of Mathematics. This course is open to Kinesiology Students who have not taken Grade 13 Calculus.
MATH 107Mathematics (For Kinesiology Students)F 3C,1T 0.5
Content similar to that of Math 106 except that it will be assumed that students have completed Grade 13 Caiculus. Accordingly, there will be broader consideration of applications.
N.B.: Not open to students in the Faculty of Mathematics.
MATH 110ACalculus 1a (For Engineering Students)F 3C,2T 0.625
Functions and their inverses, limits, continuity and derivatives. The trigonometric functions, their inverses and derivatives. Applications to rate, max./min., curve sketching problems. Sequences, the definite integral, the fundamental theorem of calculus. Applications to area and volume problems. Prereq: Grade 13 Calculus
N.B.: Not open to students in the Faculty of Mathematics
MATH 110BCalculus 1b (For Engineering Students)W,S 3C,2T 0.5
The logarithmic and exponential functions and their derivatives and applications. Elementary differential equations. Integration techniques. Improper integrals. Indeterminate forms. Arc length, average values, work, centroids and centres of mass, fluid force. Parametric and polar equations. Series of constants and tests for convergence/divergence. Power series. Taylor series. Operations on power series.
Prereq: Math 110a
N.B.: Not open to students in the Faculty of Mathematics.
Math t11a F 3C,1T 0.5
Algebra and Solid Geometry (For Science Students) Elementary Number Theory, number systems, mathematical induction, the Binomial Theorem, monotone sequences and the Cauchy criteria, polynomials.
Prereq: Grade 13 Algebra is recommended but not required.
N.8.: Not open to students in the Faculty of Mathematics.
MATH 113Calculus (For Arts and Science Students)Y 3C,2T 1.0
The derivative, differentiation of algebraic and transcendental functions. Applications of the derivative. The integral, applications of integration, techniques of integration. Power series. Polar coordinates. Some elementary differential equations. Prereq: Grade 13 Calculus
N.B.: Not open to students in the Faculty of Mathematics.
MATH 114Algebra and Vector Geometry (For Engineering Students)F 3C,2T 0.625
Matrix algebra. Systems of linear equations. Determinants. Vectors in Euclidean space, lines, pianes, spheres. Eigenvalues. Introduction to vector spaces.
Prereq: Grade 13 Algebra
N.B.: Not open to students in the Faculty of Mathematics.
MATH 115ACalculus (For Co-op Physics & Chemistry)F 30,2T 0.5
Real numbers, functions, trig functions. Limits. The derivative, differentiation, higher order derivatives, implicit functions, differentials, applications of the derivative. The definite integral. Antidifferentiation. Logarithms and exponential functions. Inverse functions.
Prereq: Grade 13 Calculus
N.B.: Not open to students in the Faculty of Mathematics.
MATH 115BCalculus (For Co-op Physics & Chemistry)W,S 3C,2T 0.5
Techniques of Integration. Improper Integrals. Indeterminate forms and L’Hépital’s rule. Infinite series. Polar co-ordinates. Partial Derivatives. Prereq: Math 115a
N.B.: Not open to students in the Faculty of Mathematics.
Functions and limits, differentiation of trigonometric, logarithmic and exponential functions, the chain rule, Rotle’s theorem, the mean value theorem, extreme value theorem, applications of the derivative, the differential, the definite integral, fundamental theorem of calculus.
Prereq: Grade 13 Cafculus
N.B.: Math 120a is not open to Honours Mathematics students.
Techniques of integration, applications of the integral, indeterminate forms, Taylor's theorem, convergence of sequences and series, power series. Prereq: Math 120a
N.B.: Math 120b is not open to Honours Mathematics students.
Systems of equations, vector spaces, matrices, determinants, geometric applications.
Prereq: Grade 13 Algebra (Math 124a is recommended, but not required)
N.B.: Math 124b is not open to Honours Mathematics students.
Math 1230a F 3C,1T 0.5
Calculus
Functions and limits, differentiation of trigonometric, logarithmic and exponential functions, the chain
. rule, Roile’s theorem, the mean value theorem, extreme value theorem, applications of the derivative, the differential, the definite integral, fundamental theorem of calculus.
Prereq: Grade 13 Calculus
N.B.: Credit will only be granted for one of Math 120a, 130a, 140a. This course may also be offered in the spring term.
Techniques of integration, applications of the integral, indeterminate forms, Taylor's theorem, convergence of sequences and series, power series. Prereq: Math 130a or 80% in Math 120a
N.8.: Credit will be granted for only one of Math 120b, 130b, 140b.
Math 140a is an advanced-level, enriched version of Math 130a.
Prereq: Grade 13 Calculus and a Grade 13 Math Average of at feast 85% (or permission of instructor) N.B.: Credit will be granted for only one of Math 120a, 130a, 140a. This course may also be offered in the spring term.
Math 144a is an advanced-level, enriched version of Math 134a.
Prereq: Grade 13 Algebra and a Grade 13 Math Average of at feast 85% (or permission of instructor) N.B.: Credit will be granted for only one of Math 124a, 134a, 144a. This course may also be offered in the spring term.
MATH 210Calculus 2 (For Chemical Engineers)F,W 3c 0.5
Partial differentiation, the gradient, muitiple integrals with applications, line and surface integrals, divergence and curl, theorems of Green and Stokes. Applications to physical problems.
Prereq: Math 110a/b
N.B.: Not open to students in the Faculty of Mathematics.
MATH 213ACalculus 2 (For Science Students)F 3C 0.5
Infinite series, Partial derivatives, chain rule, total differential, Taylor's theorem, extreme values. Prereq: Math 113 or Math 115a/b or equivalent. N.B.: Not open to students in the Faculty of Mathematics.
MATH 215Differential Equations (For Chemistry Students)F,W 3c 0.5
Complex numbers. Partial differentiation. Solution of ordinary differential equations with emphasis on special functions encountered in chemistry (Hermite and Legendre equations). Introduction to matrix algebra and eigenvalue problems.
Prereq: Math 113 or Math 115a/b or equivalent
N.B. Not open to students in the Faculty of Mathematics.
MATH 216Differential Equations (For Physics or Chemical Engineering Students)F,S 3c 0.5
Standard methods of solution. Applications to physical engineering problems. Linear equations with constant coefficients. Systems of differential equations. Solution of differential equations by the Laplace Transformation.
Prereq: Math 113 or Math 115a/b or equivalent N.B.: Not open to students in the Faculty of Mathematics.
MATH 226Elementary Differential Equations (For Science Students)Y 2C 1.0
An introduction to first order differential equations. Applications to growth, decay, reactions. Linear equations with constant coefficients. Systems of equations: vector and matrix methods. Solutions in series. Introduction to partial differential equations. Prereq: Math 113 or Math 115a/b or equivalent N.B.: Math 226 is not open to Honours or Genera! Mathematics students.
Differential catculus of functions of several variables: limits and continuity, partial derivatives, differentiability, chain rule, Taylor's formula, extreme values, mappings and Jacobians. Integral calculus of functions of several variables: multiple integrals, iterated integrals, change of variables, applications to area and volume calculations.
Prereq: Math 130b or 80% in Math 120a/b
N.B.: Credit will be granted for only one of Math 220a, 230a, 240a.
Line integrals, Green’s theorem and path independence. Sequences and series of functions: uniform convergence and power series. Introduction to ordinary differential equations: first and second order linear equations, power series solutions, applications.
Prereq: Math 230a
N.B.: Credit will be granted for only one of Math 220b, 230b, 240b.
MATH 322AIntroduction to Real AnalysisF,W,S 3C 0.5
Elementary properties of the real number system including the completeness property and its relation to the concepts of limit, continuity and differentiability; mean value theorem; Riemann integration and the integrability of continuous and monotonic functions; uniform convergence, uniform continuity and their relation to the above. The emphasis will be on applications.
Prereq: Math 220a (Math 2206 desirable)
N.B.: Math 322a is not open to Honours Mathematics students..
MATH 322BAn Introduction to Complex Variable TheoryF,W 3C 0.5
Complex numbers; continuity, differentiability, analyticity of functions; the Cauchy-Riemann equations; solutions of Lapiace’s equation; conformal mapping by elementary functions, and applications; the Cauchy and allied theorems; Taylor and Laurent expansions, uniform convergence and power series; the residue calculus, and applications. The emphasis will be on applications.
Prereq: Math 220b
N.B.: Math 3226 is not open to Honours Mathematics students..
MATH 332BAn Introduction to Complex Variable TheoryF,W 3C 0.5
Complex numbers; continuity, differentiability, analyticity of functions; the Cauchy-Riemann equations; solution of Laplace’s equation; conformal mapping by elementary functions, and applications; the Cauchy and allied theorems; Taytor and Laurent expansions, uniform convergence and power series; the residue calculus, and applications.
Prereq: Math 230b
N.B.: Credit will be granted for only one of Math 322b, 332b, PMath 352a
MATH 380AIntroduction to Information Theory with ApplicationsF,S 2C0,1T 0.5
Finite probabilistic schemes. Measures of uncertainty. Shannon's Entropy as a measure of uncertainty and expected information. Maximizing expected information. Applications to problem solving in coding, logics and linguistics.
MATH 380BInformation Theory with ApplicationsW 2C,1T 0.5
Measures of expected conditional information. Maximizing expected conditional information. Applications to communication theory and programming. Basics in questionnaire theory.