UNDERGRADUATE REGULATIONS & SYLLABUSES 2013-2014 THE FACULTY OF SCIENCE & TECHNOLOGY LEVEL: II SEMESTERS: 2 AND EVENINGS - SEMESTER 2 COURSE CODE: MATH 2110 COURSE TITLE: LINEAR ALGEBRA NUMBER OF CREDITS: 4 PREREQUISITE: MATH 1140 OR MATH 1141 AND MATH 1152 COURSE DESCRIPTION: Abstract vector spaces: Linear dependence and basis and Linear transformations and their matrices; Elementary row transformations and elementary matrices, row equivalence and rank. Solutions of systems of linear equations. Determinants, The Gram-Schmidt Orthogonalisation Process; Characteristic roots and vectors. Similarity. Diagonalisation. Quadratic forms and their reduction; The Cayley-Hamilton Theorem. Assessment: Coursework 40% Final Examination - One 2-hour written paper 60%
LEVEL: I SEMESTER: 1 & 2 COURSE CODE: MATH 1191 COURSE TITLE: INTRODUCTION TO MATHEMATICAL SOFTWARE I NUMBER OF CREDITS: 1 PREREQUISITES: TWO UNITS OF CAPE MATHEMATICS OR MATH 1125, OR EQUIVALENT COURSE DESCRIPTION: The course consists of an introduction to Excel and Maple. EXCEL Basic operations; constructing and editing formulae; changing worksheet layout; sorting and filtering. Using the Analysis Tool pack; Statistical Analysis in Excel; Intro to Visual basic. MAPLE Introduction to arithmetical operations with real numbers, integers, vectors and matrices; symbolic computation; plots, including 3d plots; solving polynomial equations and systems of linear equations; calculus and differential equations; programming in Maple. Assessment: Coursework 100%
LEVEL: II SEMESTERS: 1 AND EVENINGS - SEMESTER 1 COURSE CODE: MATH 2120 COURSE TITLE: ANALYSIS & MATHEMATICAL METHODS I NUMBER OF CREDITS: 4 PREREQUISITES: MATH 1140 AND MATH 1150 OR MATH 1141, MATH 1142, MATH 1151 AND MATH 1152 COURSE DESCRIPTION: Limits of sequences of real numbers. Convergence of series of real terms. Tests for convergence of positive series. Comparison, quotient, ratio, nth root, integral tests. Absolute convergence. The alternating series test. Power series: Functions of two (or more) real variables; limits, continuity, partial derivatives, differentiability, stationary points, Lagrange multipliers, Riemann double integral, change of variables and the Jacobian, polar, spherical and cylindrical coordinates, vector calculus, line, surface and volume integrals. Stokes and Gauss Divergence theorems. Assessment: Coursework 40% Final Examination - One 2-hour written paper 60%
LEVEL: II SEMESTERS: 1 AND EVENINGS - SEMESTER 1 COURSE CODE: MATH 2100 COURSE TITLE: ABSTRACT ALGEBRA NUMBER OF CREDITS: 4 PREREQUISITE: MATH 1140 OR MATH1141 AND MATH1152 COURSE DESCRIPTION: Fundamental concepts in Set Theory, and philosophy of sets. Relations and Functions: Algebra of permutations, Elementary Theory of Groups and Rings, group homomorphisms. Development of the number systems. Properties of the Natural Numbers, the Integers, the Rationals, the Reals and the Complex numbers. Infinite sets and their cardinalities. Transfinite arithmetic. Assessment: Coursework 40% Final Examination - One 2-hour written paper 60%
114 Return to Table of Contents Faculty of Science & Technology Online