Module Identifier MA12110 Module Title BASIC ALGEBRA Academic Year 2000/2001 Co-ordinator Dr V C Mavron Semester Semester 1 Other staff Dr V C Mavron 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.