# Module Information

Module Identifier
MA12110
Module Title
Basic Algebra
2013/2014
Co-ordinator
Semester
Intended for use in future years
Mutually Exclusive
May not be taken at the same time as, or after, MA10020.
Pre-Requisite
A or AS level Mathematics or equivalent.

#### Course Delivery

Delivery Type Delivery length / details
Lecture 22 Hours. (22 x 1 hour lectures)
Seminars / Tutorials 6 Hours. (6 x 1 hour example classes)

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (written examination)  100%
Supplementary Assessment 2 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.

### Notes

This module is at CQFW Level 4