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DEPARTMENT OF MATHEMATICS

Head: Ronald Harrop

The Department offers programs leading to the B.Sc. Degree

with a major in Mathematics or with honours in Mathematics. Several

courses

offered in these programs are ones which are also required or

considered desirable for students wishing to major or take honours in

other Science Departments or in certain Departments in the Faculty of

Arts. This applies particularly, though by no means exclusively, to

courses in the 100 and 200 series. At the graduate level the Department

offers programs leading to M.Sc. or Ph.D. Degrees in Mathematics.

REQUIREMENTS FOR STUDENTS MAJORING OR TAKING HONOURS IN MATHEMATICS

Students majoring or taking honours in Mathematics are subject to

the general regulations of the Faculty of Science. They will normally

be required by the Mathematics Department -

(1) to obtain credit by the end of their sophomore year for the

following six lower level Mathematics courses:

111-3, 112-3, 213-3

214-3, 221-2, 231-3

(a major student could defer one of 221-2, 231-3

to his junior year if he wished to do so.)

(ii) to obtain at least 50 credits in the case of honours students

and at least 30 credits in the case of major students in

upper level Mathematics courses in such a way that, both for

major and for honours students, credit is obtained for:

(a)

At least one of 411-4, 412-4, 413-4, 414-4,

(b)

421-4 and 422-4,

and

For the purpose of satisfaction of condition (ii) above, Physics 411-4

may be counted as a Mathematics course.

Foreign languages: Most graduate schools require some proficiency in

one or two foreign languages. Those who contemplate graduate studies

in Mathematics are advised to include foreign language courses in their

program.

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PRESENTATION OF COURSES

It is intended that all Mathematics courses mentioned below

will be offered at least once during the period ending with the summer semester

1967. The courses to be offered during the three semesters covered by the

present calendar are as follows:

(i)

Math

101-3, 111-3, 112-3, 213-3, 214-3

each semester

(ii)

Summer semester

1966:

Math

231-3, 412-4, 421-4, 432-4,

482-4.

Fall semester 1966:

Math

221-2, 411-4, 414-3, 422-4, 431-4,

481-3.

Spring semester 1967:

Math 231-3, 412-4, 414-4, 421-4,

424-3, 432-4, 441-4, 451-3, 461-3, 462-3, 482-4.

Graduate courses to be offered will be listed in the Graduate Calendar.

DESCRIPTION OF COURSES

Note:

The Prerequisites listed below are ones which are considered to

be normally essential on mathematical grounds. They may be waived under

special circumstances by permission of the Head of the Mathematics Department.

Mathematics

S101-3

INTRODUCTION TO STATISTICS

A pre-calculus course in random variables and their distributions, estimating

and hypothesis testing.

(2-0-2)

111-3

FUNDANTAL MATHEMATICS I

Algebra, geometry, trigonometry, introduction to calculus.

(3-1-0)

112-3

FUNDAMENTAL MATHEMATICS II

Continuation of Mathematics

111-3.

(3-1-0)

Prerequisite: Mathematics

111-3.

213-3

CALCULUS I

Differential and integral calculus with applications.

(3-1-0)

Prerequisite: Mathematics

112-3.

214-3

CALCULUS II

Continuation of work covered in Mathematics

213-3

with

introduction to ordinary differential equations.

(3-1-0)

Prerequisite: Mathematics

213-3.

221-2

INTRODUCTION TO ANALYSIS

Foundations of mathematical analysis.

(2-1-0)

Prerequisite: Mathematics 112-3.

231-3

INTRODUCTION TO ALGEBRA

Matrices, Determinants, Solution of Linear Equations.

(3-1-0)

Prerequisite: Mathematics 112-3.

411-4

METHODS I

Functions of several variables and vector field theory.

(4-1-0)

Prerequisite:

Mathematics 214-3.

412-4

METHODS II

Series, harmonic analysis, matrices and eigenvalue problems.

Some special functions.

(4-1-0)

Prerequisite:

Mathematics 214-3.

413-4

ORDINARY DIFFERENTIAL EQUATIONS

A Study of ordinary differential equations with app1icatis1 0)

Prerequisite: Mathematics 214-3.

414-4

PARTIAL DIFFERENTIAL EQUATIONS

An introductory course in partial differential equations with

applications.

(4-1-0)

Prerequisite: Mathematics 214-3.

421-4

REAL VARIABLE I

Sequeuces and series. Elementary theory of functions of a real variable.

Introduction to metric spaces.

(4-1-0)

Prerequisite: Mathematics 221-2. (With special permission 221-2 and

421-4 can be taken concurrently by persons who have at least junior standing.)

422-4

COMPLEX VARIABLE I

Complex numbers.

Functions of

a complex variable. Differentiation

and integration. Cauchy's Theorem and applications.

(4-1-0)

Prerequisite: Mathematics 2143, or else both Mathematics 213-3 and

Mathematics 221-2.

423-4

REAL VARIABLE II

Extension of subjects introduced in Mathematics 421-4 with a discussion

of Lebesgue measure.

(4-1-0)

Prerequisite: Mathematics 421-4.

424-3

COMPLEX VARIABLE II

Continuation of Mathematics 422-4 with introduction of some more

advanced aspects of complex variable theory.

(3-1-0)

Prerequisite: Mathematics 422-4.

431-4

ALGEBRA I

Linear Algebra. Vector space and matric theory.

(4-1-0)

Prerequisite: Mathematics 231-3 (with special permission 231-3 and

431-4 can be taken concurrently by persons who have at least junior

standing.)

432-4

ALGEBRA II

Algebraic systems including, for example, groups, rings.

Polynomial theory.

(4-1-0)

Prerequisite: Mathematics 213-3 or preferably Mathematics 231-3.

441-4

TOPOLOGY

Development of elementary theory of topological spaces. (4-1-0)

Prerequisite: Mathematics 213-3 or 221-2.

442-4

ELEMENTARY NUMBER THEORY

Divisibility, primes, congruences, arithmetic functions and related

topics.

(4-1-0).

Prerequisite: Mathematics 213-3 or 221-2.

451-3

MATHEMATICAL LOGIC

Introduction to the theory of formal systems and to the theory of

recursion.

(3-1-0)

Prerequisite.: Junior standing with preferably some Mathematics course

at sophomore level.

;

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461-3

VIBRATIONS AND WAVE MOTION

Dynamical behaviour of discrete and continuous systems as governed by

linear and nonlinear differential equations.

Prerequisite: Mathematics 214-3

and

preferably at least one of

Mathematics 413-4, 414-4.

462-3

CONTINUUM CHANICS I

The mechanics of deformable media emphasizing fundamental concepts

and

principles. Kinematics, conservation laws, the stress principle

and

the formulation of constitutive relations.

(3-1-0)

Prerequisite: One of Mathematics 411-4, 412-4, 413-4, 414-4.

463-4

CONTINUUM MECHANICS II

Continuation of Mathematics 462-3.

(4-1-0)

Prerequisite: Mathematics 462-3.

481-3

PROBABILITY

Events and probability measure functions. Random variables, their

distributions and characteristic functions. Limit theorems. Examples

and applications.

(3-1-0)

Prerequisite: Mathematics 213-3.

482-4

STATISTICS

Sample random variables and their distributions. Theory of estimation,

hypothesis testing, analysis of variance.

Selected additional topics.

(4-1-0) or (3-1-2)

Prerequisite: Mathematics 213-3 and preferably also Mathematics 481-3.

This latter prerequisite does not apply for Mathematics 482-4 when it is

first given, namely, in the summer semester 1966.