The

FA C U L T Y Faculty

BOOKLET 2004 – 2005 of Science & Agriculture

MATH 1170 (M 15B) INTRODUCTORY MECHANICS II (6 credits)

MATH 2120 (M 21A) ANALYSIS & MATHEMATICAL METHODS I (4 credits)

Prerequisite: A-Level Applied Mathematics Syllabus: Central forces, conservation of energy. Elementary Hydrostat- ics: Definitions, equality of pressure, transmission of pres- sure, density. Conditions of Equilibrium, surface of equal pres- sure, heterogeneous liquid. Resultant thrust, centre of pres- sure. Introduction to Hydrodynamics: Kinematics equations of motion, continuity equations, surface condition Euler’s equa- tion and applications. Mathematical modelling: Dynamics, lin-

ear and non-linear growth and decay. Examination: One 3 -hour written paper Coursework

75% 25%

MATH 2100 (M 20A) ABSTRACT ALGEBRA (4 credits)

Prerequisite: MATH 1140 (M 12A) Syllabus: Fundamental concepts in Set Theory, and philosophy of sets. Relations and Functions: Algebra of permutations, Elemen- tary 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 Com- plex numbers. Infinite sets and their cardinalities. Transfinite

arithmetic. Examination: One 3-hour written paper Coursework

75% 25%

Prerequisites: MATH 1140 and MATH 1150 (M 12A and M 12B) Syllabus: Limits of sequences of real numbers. Convergence of series of real terms. Tests for convergence of positive series. Compari- son, quotient, ratio, nth root, integral tests. Absolute conver- gence. The alternating series test. Power series: Functions of two (or more) real variables; limits, continuity, partial deriva- tives, differentiability, stationary points, Lagrange multipliers, Riemann double integral, change of variables and the Jaco- bian, polar, spherical and cylindrical coordinates, vector cal- culus, line, surface and volume integrals. Stokes and Gauss

Divergence theorems. Examination: One 2-hour written paper Coursework

70% 30%

# MATH 2140 (M 25A) INTRODUCTION TO PROBABILITY (4 credits)

Prerequisite: MATH 1140 and MATH 1150 (M 12A and M 12B) or Permission of the Head of Department

Syllabus: Basic Probability rules, including Bayes’ rule, theorem on total probability; Conditional Probability; Random Variable; Math- ematical Expectation; means, variance; Convariance of vari- ables. Variance of sum of n random variables. Chebychev’s theorem; Standard density functions and mass functions; Moment generating function. Random sample; some impor- tant statistics, sampling distributions. Central limit theorem.

# MATH 2110 (M 20B) LINEAR ALGEBRA (4 credits)

Examination:

One 2-hour written paper

60%

Coursework Examination

40%

Prerequisite: MATH 1140 (M 12A) Syllabus: Abstract vector spaces: Linear dependence and basis and Lin- ear transformations. Matrices, row equivalence and rank. So- lutions of systems of linear equations. Determinants, Charac- teristic roots and vectors. Similarity. Diagonalization. Quadratic

forms and their reduction. Examination: One 3-hour written paper Coursework

75% 25%

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