Module Identifier MA12110  
Module Title BASIC ALGEBRA  
Academic Year 2005/2006  
Co-ordinator Dr T McDonough  
Semester Semester 1  
Other staff Dr T McDonough  
Pre-Requisite A or AS level Mathematics or equivalent.  
Mutually Exclusive May not be taken at the same time as, or after, MA10020.  
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:
1. solve certain polynomial equations of small degree;
2. obtain and use relations between the roots and coefficients of polynomials;
3. compute with trigonometric functions and use trigonometric identities;
4. evaluate matrix expressions;
5. solve a system of linear equations using the Gauss-Jordan elimination process;
6. solve a system of linear equations using matrix inversion;
7. find the eigenvalues and corresponding eigenvectors of a matrix;
8. state and use the Cayley-Hamilton theorem;
9. state and use the binomial theorem.

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 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.

Content

1. POLYNOMIALS: Factors and roots. The Remainder Theorem. Relations between roots and coefficients of a polynomial.
2. TRIGONOMETRY: Trigonometric functions and identities.
3. MATRICES: Matrix operations. The solution of a system of linear equations -- Gauss-Jordan elimination process and the matrix inversion method. Eigenvalues and eigenvectors. The Cayley-Hamilton theorem.
5. SERIES: The Binomial Theorem. Convergence of the binomial series.

Reading Lists

Books
** Recommended Text
K A Stroud (2001) Engineering Mathematics 5/e. Palgrave 0333919394
** Supplementary 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

Notes

This module is at CQFW Level 4