MATH 402Topics in Mathematical Aspects of Chemistry, Biology, and the Medical Sciences

1975–76 1 calendar

Subjects will be selected from areas such as epidemiology and mathematical models of disease processes including heart disease, cancer and aging. Consideration will be given to the quantitative evaluation of the role of environmental factors important in human disease processes.

2 hours lectures

Course Descriptions

Mathematics

Undergraduate Course Descriptions

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.

12 Calculus 1

Differential and integral calculus of functions of one real variable. Transcendental functions. Integration techniques. Applications to rate, max./min., area, volume, moment, fluid pressure and work problems. Parametric and polar equations. Series of constants; power series; Taylor and Maclaurin series.

3 hours lectures, 3 hour tutorials, 2 hours labs

21 Algebra and Vector Geometry

Complex numbers. Matrix algebra. Systems of linear equations. Vectors in Euclidean space, lines, planes, hyperplanes, spheres. Determinants. Subspaces of Cartesian space and matrices. Linear transformations, eigenvalue problems. Linear programming.

3 hours lectures, I hour problems

22 Calculus 2 (For Chemical Engineers)

Partial differentiation, the gradient, multiple integrals with applications, line and surface integrals, divergence and curl, theorems of Green and Stokes. Applications to physical problems.

3 hours lectures, one term

25 Calculus 2 (For Electrical Engineers)

Differential calculus of functions of several variables. Differential equation. Multiple integrals. Prerequisite: M12 or equivalent

31 Differential Equations

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.

3 hours lectures

32 Numerical Analysis

A survey of numerical procedures with emphasis upon computer implementation using the FORTRAN 1V programming language. Topics include: interpolation, curve fitting, solution of non-linear equations, numerical integration, numerical solution of ordinary and partial differential equations, matrix algebra and solution of systems of linear equations.

2 hours lectures, 2 hours problems, one term

Offered in the Fall and Spring terms

35 Advanced Calculus (for Electrical Engineers) Fourier series. Partial differential equations: sepa- . ration of variables, wave equations, heat equation and Laplace’s equation. Fourier integral. Properties of complex analytic functions. Complex integration. 2 lectures, 1 hour problems, one term

44 Complex Variable

Cauchy-Reimann equations, the Cauchy integral theorems, conformal mapping, the Taylor and Laurent series, contour integration.

2 lectures, ] hour problems, one term

§1 Probability and Statistics

Frequency distributions; probability; Binomial, Normal, 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.

3 lectures, 2 hours problems, one term

§2 Applied Probability and Statistics

(for Mechanical Engineers)

Axiomatic development of probability. Conditional probability, Bayes’ Theorem and independence. Permutations and combinations as related to probability. Discrete and continuous random variables. Special cases of uniform, binomial, Poisson, normal, etc. distributions. Mathematical expectation and moment generating functions, Derived distributions. Sampling from a normal population. Elements of decision theory. Various methods of estimating parameters and testing hypotheses. °

3 hours lectures, I hour tutorial, one term

73a Introduction to Solving Business Problems - by Computer

An introduction to algorithms with emphasis on the solution of mathematical problems arising in the business world. Concept and properties of an algorithm, language and notation for describing algorithms. Analysis of problems, development of models and algorithms for their solution; implementation in procedure oriented languages (FORTRAN IV and BASIC) and the execution of these programs using several computing facilities.

2 hours lectures, 2 hours tutorial, one term

Offered in the Fall and Winter terms

, Course Descriptions . 363

Mathematics

73b Modelling & Simulation for Business Applications

This course is intended to introduce students to the techniques of modelling, simulation asd analysis of business systems. Simulation is developed as an effective tool for studying various types of business system environments. Students will be required to develop and run simulation models using both GPSS and dynamo programming languages.

3 hours lectures, Winter term

73c The Computing Process

This course is designed for the student who will encounter computing facilities in his or her career and must have an understanding of the terminology, hardware (computing machinery), software (computer programs), and financial and management aspects of the computing process. Topics include: historical development of computing machinery and programming languages; methods of job processing; development/ maintenance of application programs; organization and management of a computer installation; uses of specialized applications packages.

2 hours lectures, Winter term

364 ..

73d Introduction to File Processing

File processing is an integral part of most commercial applications, This course will give a thorough introduction to the most common file processing techniques such as file maintenance, sorting and report generation. Language and notation for describing such algorithms. Analysis of problems dealing with files, and develo-ment of ‘algorithms for their solution. Introduction to procedure-oriented: languages (usually COBOL) for solving such problems.

2 hours lectures, 2 hours tutorial (laboratory).

Fall term

Prerequisite: M302 or consent of the instructor

Note

Prerequisite: An introductory programming course

Note This course is cross listed in Management Sciences as MS2!.

Note Math 73a is a prerequisite for Math 73b, 73c and 73d

Note Only one of Math 73a, 112a and 122a can be taken for credit.

Note Math 73a cannot be counted for credit towards a B.Math degree.

Prerequisite: Math 73a or the equivalent. An introductory statistics course

Note Math 73b cannot be counted for credit toward a B.Math degree.

Prerequisite: Math 73a or the equivalent

Note Math 73c was formerly called Math 72b.

Note Only one of Math 73c, 112b can be taken for credit.

Note Math 73c cannot be counted for credit towards a B.Math degree.

Prerequisite: Math 73a or the equivalent

Note Math 73d was formerly called Math 72a.

Note Credit wiil only be granted for one of Math 73d or

• 1975–76 PDF p. 363

1974–75 1 calendar

Titled Topics in Mathematical Aspects of Chemistry, Biology, and the Medical Sciences Note 12 Calculus 1 21 Algebra and Vector Geometry 22 Calculus 2 (for Chemical Engineers).

Subjects will be selected from areas such as epidemiology and mathematical models of disease processes including heart disease, cancer of aging. Consideration will be given to the quantitative evaluation of the role of environmental factors important in human disease processes. ‘ 2 hours lectures Prerequisites: M302 or consent of the instructor

Undergraduate Course Descriptions

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.

Functions and limits, the derivative, Differentiation formulae, Applications to tangents, rates, extrema. Antiderivatives. The ' definite integral, fundamental theorem of integral calculus. ‘Applications to area, volume, moments, fluid pressure, work, potential. Transcendental functions. Techniques of integration. Parametric and polar equations with applications. Mean value theorem. Introduction to partial derivatives. Introduction to differential equations with applications.‘ Students will work selected problems under supervision. 2 hours lectures, 1-2 hours problems.

Sets, subsets, relations, functions. Mathematical induction. Limits of real sequences. Vector geometry of points, lines, planes and spheres. Arithmetic of complex numbers. Introductory material on systems of linear equations. Systems of linear equations, Gaussian Elimination. Matrices, augumented matrix, row-reduced matrices, elementary matrices, inverses. Vector spaces, spanning sets, bases, dimension. Rowspace, column-space, null-space, rank. Determinants. Linear transformations. Eigenvalues and Eigenvectors. Functions of complex variables. 2 hours lectures, 1-Y2 hours problems

Partial differentiation, the gradient, multiple integrals with applications, line and surface integrals, divergence and curl, Theorems of Green and Stokes. Applications to physical problems. 3 hours lectures, one term

25 Calculus 2 (for Electrical Engineers)

31 Differential Equations

32 Numerical Analysis

35 Advanced Calculus (for Electrical Engineers)

44 Complex Variable

51 Probability and Statistics

52 Applied Probability and Statistics (for Mechanical Engineers)

Faculty of Mathematics

Differential calculus of functions of several variables. Differential Equations. Multiple integrals. Prerequisite: M12 or equivalent

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.

3 hours lectures

A survey of numerical procedures with emphasis upon computer implementation using the FORTRAN IV programming language. In particular, the following topics are introduced: interpolation, curve fitting, solution of non-linear equations, numerical integration, numerical solution of ordinary differential equations, matrix algebra and solution of systems of linear equations, and problems in the solution of partial differential equations.

2 hours lectures, 2 hours problems, one term

Offered in the Fall and Spring terms

Credit will not be granted for both M32 and M240 (a)

Fourier series. Partial Differential Equations; separation of variables, wave equations, heat equation and Laplace’s equation. Fourier integral. Properties of complex analytic functions. Complex integration.

Cauchy-Riemann equations, the Cauchy integral theorems, conformal mapping, the Taylor and Laurent series, contour integration.

2 lectures, 1 hour problems, one term

Frequency distributions; probability; Binomial, Normal, Poisson laws. Sampling theory. Distribution of Chisquared, F, and t. Hypothesis testing, quality control, regression theory. Curve fitting. Analysis of variance, introduction to experimental design. 3 lectures, 2 hours problems, one term

Axiomatic development of probability. Conditional probability, Bayes’ Theorem and independence. Permutations and combinations as related to probability. Discrete and continuous random variables. Special:cases of uniform, binomial, Poisson, normal, etc. distributions. Mathematical expectation and moment generating functions. Derived distributions. Sampling from a normal population. Elements of decision theory. Various methods of estimating parameters and testing hypotheses.

3 hours lectures, 1 hour tutorial, one term

This course is cross listed in Management Science as MS21.

61 Applicable Mathematics

for Systems Design 1 (Also Listed as Systems Design 211)

62 Applicable Mathematics for Systems Design 2 (Also listed as Systems Design 212)

- 72 (a) Introduction to Computer Science in Business and Economics

72 (b) Advanced Topics in Computer Science in Business and Economics

81 Introduction to Functions Analytic Geometry, and Calculus

Faculty of Mathematics 525

First order differential equations, integrating factor, higher order differential equations. Complex variables, forced and free solutions to differential equations, transient and steady state solutions, applications. Fourier series, Fourier transforms and applications.

Laplace transforms. Solution of ordinary linear differential equations by Laplace transforms, applications. Residue calculus and its relation to inverse Laplace transforms. Functions of the complex variable. Difference equations. Z transforms.

The purpose of Math 72 (a) is to introduce the student to the basic concepts of programming electronic digital computers. Students are taught to write computer programmes in two of the most widely used computer languages in the business world, namely COBOL and FORTRAN. The first part of the course deals with the COBOL language and uses this language to write programmes to simulate a large-scale credit card system. Students are shown how computers are employed to write invoices, process customer accounts and mail out credit cards. The second half of the course uses FORTRAN to handle problems involving inventory control, simulation of business problems and plotting.

2 hours lectures, 1 hour tutorial, one term

Offered in the Fall and Winter terms

Credit will only be granted for one of M72, M112, M122 or M132. M72 cannot be counted as a credit towards a B.Math degree..

Topics discussed will include.

a) An introduction to machine hardware — CPU’s, channels, tape drives, disk drives, main memory, slow core, drums, etc. Basic machine configurations will also. be discussed. The relative costs involved will be covered whenever possible.

b) The concept of an operating system, JCL, compilers and system software packages.

c) Some of the basic terminology such as multiprogramming, batch processing, timesharing, telecommunications and data bases. d) The general organization of a computing centre and the position of computer centres in corporate structures.

2 hours lectures, 1 hour tutorial, one term.

Offered in the Winter term

Credit will only be granted for one of M72, M112, M122 or M132. M72 cannot be counted as a credit towards a B.Math degree..

Polynomial functions. Inverse of a function. Rational functions. Exponential functions and identities. The straight line. Conic sections. Problems solved by analytic means. Simple transformation. The limit concept and an introduction to Calculus including the derivative and its application to graph sketching.

2 hours lectures ‘

\

526 § 82 Introduction to Algebra 83 Introductory Mathematics for Sociology : Students 84 Algebra 85 Mathematics for Environmental Studies

Faculty of Mathematics

Properties of real numbers including inequalities and absolute value. Systems of equations in two and three variables including linear, quadratic, and cubic equations. Complex numbers and polar representation. Exponents. Permutations and combinations. The Binomial Theorem. Sequences and series. 2 hours lectures

Set Theory, Permutations and Combinations, Vectors and Matrices, Probability Theory, Solution of Linear Equations, Game Theory, Linear Programming. 2 hours lectures, 2 hours problems lab (alternate weeks) 2 terms

A special course designed for students in Psychology and related subjects. Polynomial, rational, exponential and trigonometric functions. Elementary analytical geometry. Polar co-ordinates. Fundamental concepts in the Calculus. Linear and quadratic systems of equations. Vectors, complex numbers. Mathematical Induction Permutations and combinations, the. Binomial theorem. 2 hours lectures, 2 hours problems lab (alternate weeks) Winter term only

Quantitative analysis in environmental research. Elementary concepts in Algebra, notation, terminology, operations. Introductory matrix algebra. Probability Theory. Permutations and Combinations, approaches to probability, dependent and independent events, conditional probability, Markov processes, distribution functions, including the Binomial, Poisson and Normal distributions, with applications to problems in Environmental Studies. 2 hours lectures, one term Winter term only

Note

Note

Prerequisite: An introductory programming course

Note

Note

Prerequisite: M72 (a) or the equivalent

• 1974–75 PDF p. 518

1971–72 to 1973–74 3 calendars

Titled Topics in Mathematical Aspects of Chemistry, Biology, and the Medical Sciences Note ,.

Subjects will be selected from areas such as introductory wave mechanics, spectroscopy, molecular biology, and mathematical models of disease processes. 2 hours lectures.

402 may not be counted as a Mathematics credit, but may be counted as an elective credit.

• 1971–72 PDF p. 358
• 1972–73 PDF p. 439
• 1973–74 PDF p. 474