UNDERGRADUATE REGULATIONS & SYLLABUSES 2013-2014 THE FACULTY OF SCIENCE & TECHNOLOGY LEVEL: II SEMESTERS: 2 AND EVENINGS - SEMESTER 2 COURSE CODE: MATH 2160 COURSE TITLE: ANALYSIS & MATHEMATICAL METHODS II NUMBER OF CREDITS: 4 PREREQUISITES: MATH 1140 AND MATH 1150 OR MATH 1141, MATH 1142, MATH 1151 AND MATH 1152 COURSE DESCRIPTION: The Laplace transform and applications to differential and integral equations. Ordinary linear differential equations, Wronskian, linear independence. Existence and uniqueness (no proofs). Classification of points of second-order differential equations. Series solutions about ordinary and regular singular points. Fourier series. Solution of the twodimensional heat, wave and Laplace equation using the separation of variables technique. Functions of a single complex variable, continuity, differentiability, analyticity and the Cauchy-Riemann equations; power series and contour integrals, Cauchy’stheorem and integral formulae. Singularities and their classification. Residue theorem and its application to the evaluation of definite integrals. Assessment: Coursework 40% Final Examination - One 2-hour written paper 60%
LEVEL: II SEMESTERS: 1 AND EVENINGS - SEMESTER 1 COURSE CODE: MATH 2140 COURSE TITLE: INTRODUCTION TO PROBABILITY NUMBER OF CREDITS: 4 PREREQUISITES: MATH 1140 OR MATH 1150 OR MATH 1141 AND MATH 1152 OR MATH 1142 AND MATH 1151 COURSE DESCRIPTION: Basic Probability rules, including Bayer’s rule, theorem on total probability; Conditional Probability; Random Variable; Mathematical Expectation; means, variance; Convariance of variables. Variance of sum of n random variables. Chebychev’s ís theorem; Standard density functions and mass functions; Moment generating function. Random sample; some important statistics, sampling distributions. Central limit theorem. Assessment: Coursework 40% Final Examination - One 2-hour written paper 60% LEVEL: II SEMESTERS: 2 AND EVENINGS - SEMESTER 2 COURSE CODE: MATH 2150 COURSE TITLE: INTRODUCTION TO STATISTICS NUMBER OF CREDITS: 4 PREREQUISITES: MATH 2140 OR MATH 3110 COURSE DESCRIPTION: Theory of Estimation: Ideas of point estimation; mean-squared error; interval estimation; method of maximum likelihood; Cramer-Rao Inequality. Hypothesis Testing: Type I and Type II errors; tests concerning means, variances and proportions; Goodness of fit Tests; non-parametric tests. Ideas of Regression Analysis including simple linear Regression in detail; Experimental Design and the Analysis of Variance (Completely Randomised Design, Block Designs, Latin Squares, Factorial Designs). Assessment: Coursework 40% Final Examination - One 2-hour paper 60%
LEVEL: II SEMESTER: 1 COURSE CODE: MATH 2170 COURSE TITLE: INTRODUCTION TO COMBINATORICS NUMBER OF CREDITS: 4 PREREQUISITE: MATH 1140 OR MATH 1141 AND MATH 1152 COURSE DESCRIPTION: Permutations and Combinations. The Inclusion - Exclusion Principle. Linear equations with unit coefficients; Recurrence relations; Generating functions; Geometry of the plane; Colouring problems; Combinatorial probability. Partitions of integer; Random walks; Designs. Assessment: Coursework 25% Final Examination - One 2-hour written paper 75% LEVEL: II SEMESTER: 2 COURSE CODE: MATH 2180 COURSE TITLE: INTRODUCTION TO OPTIMIZATION NUMBER OF CREDITS: 4 PREREQUISITE: MATH 1140 OR MATH 1141 AND MATH 1152 COURSE DESCRIPTION: Graphs and Digraphs; Ranking; Shortest Path; Communication Networks; Convex sets; Linear programming; Simplex Method; Theory of games. Assessment: Coursework Examination 25% Final Examination - One 2-hour written paper 75% 115 Return to Table of Contents Faculty of Science & Technology Online