(from pages 61-64 of the printed calendar)

(page 61)

Associate Professors | - | J. D. Hiscocks, L. G. Hoye |

Lecturer | - | D. M. Connolly |

Sessional Lecturer and Tutorial Assistant - J. Haig |

The Department offers courses in Mathematics and Statistics leading to a B.Sc. in Mathematics.

The minimal B.Sc. graduation requirement consists of successful completion of four semesters of the Analysis sequence, namely, Mathematics 1030, 2070, 2080, and 2090 and at least four additional semesters of work in any combination of Algebra, Statistics or Applied Mathematics for which the student possesses the appropriate pre- and corequisites. Courses in Statistics may be counted toward a Major concentration in Mathematics.

Students anticipating a Major concentration in Mathematics or considering graduate work in Mathematics should consult the Department at an early stage concerning their choice of undergraduate courses.

**Mathematics 901. Elementary Mathematics** (2-0) F-S

Review of basic mathematics, introduction to trigonometric functions and equations.

NOTE: This course does not carry credit toward a degree.

**Mathematics 1030. Introduction to Mathematics** (3-2) F-S

Logic, methods of proof, sets. Real numbers. Relations, functions. Limits, continuity. Tangents to curves, derivatives. Explicit and implicit functions. Parametric equations. Maxima and minima. Applications.

Prerequisites: Mathematics 30 and 31. Those students lacking the prerequisites should consult the department in advance of registration in order to make arrangements for supplementary work.

**Mathematics 2070. Calculus I** (3-2) S

Summation, definite and indefinite integrals, area, volume. Exponential, logarithmic, trigonometric and hyperbolic functions, methods of integration, improper integrals.

Prerequisite: Mathematics 1030.

(page 62)

**Mathematics 2080. Calculus II** (3-2) F

Geometry of various co-ordinate systems. Conic sections. Vectors in three dimensions, scalar and vector products, vector derivatives. Curves and surfaces. Partial differentiation, tangent planes, normal lines, directional derivatives, gradients.

Prerequisite: Mathematics 2070.

**Mathematics 2090. Calculus III** (3-2) S

Elements of differential equations. Double and triple integrals. Infinite series, tests of convergence, power series and Taylor's formulas. Determinants.

Prerequisite: Mathematics 2080

**Mathematics 2410. Linear Algebra I** (3-0) F

Abstract systems, vectors, linear dependence, vector spaces, bases and dimension, Euclidean n-space. Linear transformations, matrices, determinants.

Prerequisite: Mathematics 1030.

**Mathematics 2420. Linear Algebra II** (3-0) S

Matrices and linear transformations, rank of a matrix, bilinear and quadratic forms, polynomials, over the complex field, factorization, characteristic values and vectors, similarity of matrices.

Prerequisite: Mathematics 2410.

**Mathematics 2810. Introduction to Differential Equations** (3-0) F

Methods of solution of ordinary differential equations including exact, separable, linear homogeneous equations, power series solutions. Basic theory of linear systems.

Prerequisite: Mathematics 2070.

Corequisite: Mathematics 2080.

**Mathematics 2820. Intermediate Differential Equations** (3-0) S

Numerical methods. Laplace transforms. Existence and uniqueness of solution, theory of linear differential equations.

(page 63)

Fourier series. Non-linear differential equations. Introduction to partial differential equations.

Prerequisite: Mathematics 2810.

Corequisite: Mathematics 2090.

**Mathematics 3030. Advanced Calculus** (3-0) F

Brief review of single variable calculus. Differential and integral calculus of many variables. Vector differential and integral calculus. Partial differentiation, implicit function theorems.

Prerequisite: Mathematics 2090.

**Mathematics 3040. Elementary Analysis** (3-0) S

Infinite series, uniform convergence. Power series. Fourier series and integrals. Elements of analysis, point set theory, fundamental theorems on continuous functions, theory of integration.

Prerequisite: Mathematics 3030.

**Mathematics 3410. Algebraic Structures I** (3-0) F

Sets, fundamental number systems, natural numbers, integers, rationals, reals. Congruence. Congruence classes. Isomorphisms, homomorphisms. Introduction to groups, rings, domains, fields.

Prerequisite: Mathematics 2410.

**Mathematics 3420. Algebraic Structures II** (3-0) S

Polynomial rings, ideals. Quadratic residues. Galois fields. Modular systems, vector spaces.

Prerequisite: Mathematics 3410.

**Mathematics 3980. Reading Course on Topics in Mathematics** (3-0) F

Note: The content may vary widely from year to year.

Prerequisite: Consent of Department.

**Mathematics 3990. Reading Course on Topics in Mathematics** (3-0) S

Note: The content may vary widely from year to year.

Prerequisite: Consent of Department.

(page 64)

**Statistics 2770. Statistics** (3-2) F

Descriptive statistics. Measures of location and dispersion. Elementary probability. Binomial, normal and Poisson distributions. Inference from large and small samples. Chi-square, F and t-tests. Linear regression and correlation.

Prerequisite: Mathematics 1030.

**Statistics 3780. Mathematical Probability** (3-0)

Probability spaces. Binomial, hypergeometric, Poisson, exponential, gamma and normal distributions. Mathematical expectation. Method of moments, moment generating functions. Random variables. Markov chains.

Prerequisites: Statistics 2770 and Mathematics 2090.

(Not offered 1967-68.)

**Statistics 3790. Mathematical Statistics** (3-0)

Sampling. Estimation. Theory and application of hypothesis testing. Distribution of the mean. Chi-square F and t-distributions. Central limit theorem. Confidence intervals. Regression and correlation. Analysis of variance.

Prerequisite: Statistics 3780.

(Not offered 1967-68.)