Module Identifier MA12110
Module Title BASIC ALGEBRA
Co-ordinator Dr T McDonough
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
Course delivery Lecture   22 x 1 hour lectures
Seminars / Tutorials   6 x 1 hour example classes
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

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.

Brief 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 trigonometric functions and identities, roots of polynomial equations, the binomial theorem, simple matrix algebra and solution of linear equations by row reduction of matrices.

Aims

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

Content

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, determinants, adjoints and inverses, the Cayley-Hamilton theorem.
4. SERIES: The Binomial Theorem and the binomial series.