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.

**Reading Lists**

**Books**
**** Recommended Text**

M M Nicolson.
*Fundamentals and Techniques of Mathematics for Scientists*. Longman

P G Andres, H J Miser & H Reingold.
*Basic Mathematics for Engineers*. Wiley
**** Supplementary Text**

G Stephenson.
*Mathematical Methods for Science Students*. Longman

A Jeffrey.
*Mathematics for Engineers and Scientists*. Van Nostrand Reinhold