MA12110 - BASIC ALGEBRA

Module Identifier	MA12110
Module Title	BASIC ALGEBRA
Academic Year	2001/2002
Co-ordinator	Dr V Mavron
Semester	Semester 1
Pre-Requisite	A or AS level Mathematics or equivalent.
Mutually Exclusive	May not be taken at the same time as, or after, any of MA10020, MA11010, MA12510, MA12610
Course delivery	Lecture	22 x 1 hour lectures
	Seminars / Tutorials	6 x 1 hour example classes
Assessment	Exam	2 Hours (written examination)	100%
	Resit assessment	2 Hours (written examination)	100%

General description

The purpose of this module is to present some of the basic concepts of algebra at a level suitable for applications in other areas. The syllabus includes the solution of polynomial equations, complex numbers, trigonometric functions, graphs. The binomial theorem and solution of linear equations by row reductions of matrices.

Aims

To introduce students to algebraic ideas, at a level suitable for application in subjects other than Mathematics.

Learning outcomes

On completion of this module, a student should be able to:

manipulate trigonometric functions and use trigonometric identities;
solve certain polynomial equations;
manipulate matrices;
solve a system of linear equations using row reduction of matrices;
find the eigenvalues and corresponding eigenvectors of a matrix;
form inverse functions;
use the binomial theorem and the binomial series.

Syllabus

1. TRIGONOMETRY: Trigonometric functions and identities.
2. POLYNOMIALS: Factors and roots, the Remainder Theorem and the Factor Theorem, relationships between roots and coefficients.
3. MATRICES: Matrix operations, the solution of a system of linear equations, eigenvalues and eigenvectors.
4. MAPPINGS: Injective, surjective and bijective mappings, inverse functions.
5. SERIES: The Binomial Theorem and the binomial series.

Reading Lists

Books
** Recommended Text
M M Nicolson. Fundamentals and Techniques of Mathematics for Scientists. Longman B6122851
P G Andres, H J Miser & H Reingold. Basic Mathematics for Engineers. Wiley X801151197
** Supplementary Text
G Stephenson. (1973) Mathematical Methods for Science Students. 2nd. Longman 0582444160
A Jeffrey. Mathematics for Engineers and Scientists. Van Nostrand Reinhold 0442306520