Department:Mathematics and Statistics
Course Convenor:Dr ML MacDonald
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Curriculum Design: Outline Syllabusback to top
Matrices: addition and multiplication, transpose and inverse.
Simultaneous linear equations
Reduction to echelon form by elementary row operations
Determinants: expansions about a row or column
Elementary row and column operations on determinants
Properties of determinants
Linear transformations of Euclidean space
The matrix of a linear transformation
Non-singular linear transformations
Eigenvectors and eigenvalues
The characteristic equation
Curriculum Design: Pre-requisites/Co-requisites/Exclusionsback to top
A-level Mathematics at A-grade or above, or equivalent.
Educational Aims: Subject Specific: Knowledge, Understanding and Skillsback to top
The specific aim of this module is to introduce the notion of matrices and their basic uses, mainly in algebra.
The main goals are to learn how the algorithm of elementary row and column operations is used to solve systems of linear equations, the concept and use of determinant, and the notion of a linear transformation of the euclidean space. The course also aims at defining the main concepts underlying linear transformations, namely singularity, the characteristic equation and the eigenspaces.
Educational Aims: General: Knowledge, Understanding and Skillsback to top
The aim of this module is to give an introduction to the theory of matrices together with some basic applications. These are needed for later courses, such as linear algebra, and they are also of practical use for applications to geometry.
Learning Outcomes: Subject Specific: Knowledge, Understanding and Skillsback to top
The student will learn the important algebraic concepts that are matrices, determinants and linear transformations, together with their applications in mathematics, with an emphasis in algebra.
The student will also know how to solve a system of linear equations, how to express a linear transformation of the real euclidean space using a matrix, from which the student will be able to determine whether it is singular or not and obtain its characteristic equation and eigenspaces.
At the end of this module, the student will have understood how to work with matrices, in particular by means of elementary row and column operations, and how they can be used to solve systems of linear equations with or without parameters.
Learning Outcomes: General: Knowledge, Understanding and Skillsback to top
The student will learn the elementary theory pertaining to matrices and their applications in mathematics, including solving systems of linear equations, determinants and linear transformations. At the end of this module, the student will have understood how these algebraic notions may relate to each other, and he/she will have learned the basic algorithms which allow their analysis.
Assessment: Details of Assessmentback to top
Assessment will be through:
(i) weekly coursework, aimed at testing and consolidating understanding of the basic elements of the course;
(ii) a test at the end of the module which assesses the students' understanding through short questions;
(iii) an examination in the Summer which assesses more fully the students' understanding and summative knowledge of the topics.
Curriculum Design: Select Bibliographyback to top
GILBERT, J. and JORDAN, C. (2002) Guide to Mathematical Methods, Second Edition. Palgrave Macmillan.
TOWERS, D.A. (1990) Guide to Linear Algebra. CRC Mathematical Guides.