Fall term  Introduction to real numbers. Real sequences. Functions: algebraic, exponential and trigonometric functions and their inverses. Limits, continuity and derivatives. Rules for differentiation. Main theorems of the differential calculus. L'Hôpital's rule. Applications of derivatives.

Winter term Antidifferentiation: all basic methods. Definition of the integral, Riemann sums and fundamental theorem of calculus. Improper integrals. Applications of integration. Plane polar and 3-dimensional coordinates. Computer laboratory using MAPLE symbolic computation software to illustrate concepts and solve problems in calculus.

MAE101(1): Refers to the Fall term of this course (1 credit)

MAE101(2): Refers to the Winter term of this course (1 credit)

Only offered through the Division of Continuing Studies.

This course provides a non-calculus treatment of topics in Probability and Statistics. Lessons include a brief review of set operations, definitions and examples of sample space and probability of events, random variables, various discrete and continuous distributions, mean, variance and general expectations, sampling, tests of hypothesis for mean and variance, and power of tests.

Note : Distance Learning computer system requirements

This course includes an introduction to sets, set notation, the properties of real numbers and the real number system. It also covers various topics in algebra including factoring algebraic expressions and arithmetic operations involving polynomial, rational and exponential expressions.  Principal roots are covered, as is the connection between exponential and radical notation. The properties of inequalities and absolute values are introduced, and techniques for solving linear, non-linear and absolute value equalities and inequalities are presented. The material on functions includes the combination and composition of functions and the determination of the domain of combined and composed functions.  Inverse functions are examined, and the properties of logarithmic and exponential functions are studied along with some applications to "real-world" problems.

Also offered through the Division of Continuing Studies.

Elementary logic. Introduction to sets and operations on sets. Combinations and permutations. Discrete probability.

Note : Distance Learning computer system requirements

Only offered through the Division of Continuing Studies.

Review of basic algebra including powers and logarithms. The real number system, open and closed intervals, solution of inequalities. Functions and their properties. Definition of the limit and continuity of a function at a point. Limits at infinity. The intermediate value theorem. Graphs of continuous and discontinuous functions. Exponential and logarithmic functions, their graphs, properties and applications. Definition of the derivative as a limit. The mean value theorem. Derivatives of sums, products and quotients of functions. Composite functions and the chain rule. Derivatives of second and higher order. Application of differential calculus to graph sketching, optimization problems, approximation of functions and marginal analysis.

Note : Distance Learning computer system requirements

This course is intended to emphasize the basic concepts of Calculus: functions, limits, derivatives and integrals. Students will be introduced to the use of mathematical software to carry out computations.

Part I: Differential Calculus. Limits and continuity. Defnition of a derivative. Derivatives of polynomials, exponential and logarithmic functions. Basic diferentiation: product, quotient and chain rules. Second order derivatives and convexity. Extreme points, optimization and application to business and economics.

Part II: Integral Calculus. Anti-derivatives and some basic rules of integration. The defnite integral as an area and the Fundamental Theorem of Calculus. Application of the defnite integral to business and economics.

Vectors in 2 and 3 dimensions. Dot products, orthogonality. Lines and planes in three-space. Introduction to complex numbers. Systems of linear equations. Matrix algebra. Determinants. Finite-dimensional real vector spaces, subspaces, bases and dimension. Eigenvalues, eigenvectors, diagonalisation of matrices.

A second version of this course will be available (in English only) for students with a weaker background, in which there will be an additional lecture period. (Contact hours: 4 - 1 - 4)

Vectors in 2, 3 and higher dimensions; geometric applications.  Linear systems of equations. Matrices: matrix algebra, inverses and determinants. Solution of matrix equations. Integers: GCD, LCM, division algorithm, integers modulo n, RSA encryption. Complex numbers, arithmetic, powers and roots. Fundamental theorem of algebra and solution of polynomial equations.

Only offered through the Division of Continuing Studies.

Introduction to the real numbers. Functions: algebraic, exponential and trigonometric and their inverses. Limits, continuity and derivative. Rules for differentiation. Main theorems of the differential calculus. L'Hospital rule. Applications of derivatives.

Note : Distance Learning computer system requirements

Only offered through the Division of Continuing Studies.

Antidifferentiation : techniques of integration. Riemann sums, definition of the integral and fundamental theorem of Calculus. Improper integrals. Applications of integration. Polar coordinates. First and second order linear differential equations.

Note : Distance Learning computer system requirements

Also offered through the Division of Continuing Studies.

The subject of this course is the design, analysis and implementation of algorithms. It examines the relationship between problem solving and algorithms, the design of algorithms using pseudocode; sequence, selection and iteration; and abstraction (functions), and the correctness and efficiency of algorithms. Algorithms for tasks such as searching, sorting and pattern matching will be introduced and analyzed. Algorithms will be implemented in a high-level programming language as programs using appropriate data types, statements and methods. The use of compilers, interpreters and virtual machines in executing programs will be studied. An introduction to object-oriented programming, classes and objects will be given.

Note : Distance Learning computer system requirements